Exhibit 99 (a)(1)(v)

HENNESSY ADVISORS, INC.

Offer to Purchase for Cash
Of Up to $25.0 million in Aggregate Value of its Common Stock
At a Purchase Price of $25.00 per Share

THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., NEW YORK CITY TIME, ON SEPTEMBER 18, 2015, UNLESS THE OFFER IS EXTENDED OR WITHDRAWN (SUCH DATE, AS IT MAY BE EXTENDED, THE “EXPIRATION DATE”).

August 20, 2015

To Our Clients:

Enclosed for your consideration are the Offer to Purchase, dated August 20, 2015 (the “Offer to Purchase”), and related Letter of Transmittal (which together, as they may be amended or supplemented from time to time, constitute the “Offer”) in connection with the offer by Hennessy Advisors, Inc., a California corporation (“Hennessy” or the “Company”), to purchase for cash up to $25.0 million in aggregate value of its Common Stock, no par value per share (the “Shares”), at a price of $25.00 per Share, net to the seller in cash, less any applicable withholding taxes and without interest, upon the terms and subject to the conditions set forth in the Offer to Purchase and the related Letter of Transmittal. Capitalized terms used herein and not defined herein shall have the meanings given to them in the Offer to Purchase. The description of the Offer in this letter is only a summary and is qualified by all of the terms and conditions of the Offer set forth in the Offer to Purchase and Letter of Transmittal.

Upon the terms and subject to the conditions of the Offer, if, $25.0 million in aggregate value of the Company’s Common Stock or less is properly tendered and not properly withdrawn, Hennessy will buy all Shares properly tendered and not properly withdrawn. However, because of the “odd lot” priority, proration and conditional tender provisions described in the Offer to Purchase, Hennessy may not purchase all of the Shares tendered if, based on the Purchase Price, Shares having an aggregate value in excess of $25.0 million are properly tendered and not properly withdrawn. Under no circumstances will interest be paid on the purchase price for the Shares, regardless of any delay in making such payment. Shares not purchased in the Offer will be returned to the tendering shareholders at Hennessy’s expense promptly after the Expiration Date.

Hennessy reserves the right, in its sole discretion, to change the Purchase Price and to increase or decrease the aggregate value of Shares sought in the Offer, in each case subject to applicable law. Hennessy reserves the right, in its sole discretion, to terminate the Offer upon the occurrence of certain conditions more specifically described in Section 7 of the Offer to Purchase, or to amend the Offer in any respect, in each case subject to applicable law.

Upon the terms and subject to the conditions of the Offer, if, based on the Purchase Price, Shares having an aggregate value in excess of $25.0 million (or such greater amount as Hennessy may elect to pay, subject to applicable law) have been properly tendered and not properly withdrawn before the Expiration Date, Hennessy will purchase Shares in the following order of priority: (i) first, from all holders of “odd lots” of less than 100 Shares who properly tender all their Shares and do not properly withdraw them before the Expiration Date (partial tenders will not qualify for this preference); (ii) second, from all other shareholders who properly tender Shares and do not properly withdraw them before the Expiration Date, on a pro rata basis, subject to the conditional tender provisions described in the Offer to Purchase and with appropriate adjustment to avoid purchases of fractional Shares; and (iii) third, only if necessary to permit Hennessy to purchase $25.0 million in aggregate value of Shares (or such greater amount as Hennessy may elect to pay, subject to applicable law), from holders who have tendered Shares subject to the condition that a specified minimum number of the holder’s Shares be purchased if any Shares are purchased in the Offer as described in the Offer to Purchase (for which the condition was not initially satisfied) and who have not properly withdrawn them before the Expiration Date, by random lot, to the extent feasible. To be eligible for purchase by random lot, shareholders whose Shares are conditionally tendered must have tendered all of their Shares. Therefore, it is possible that fewer than all Shares tendered by a shareholder will be purchased or that, if a tender is conditioned upon the purchase of a specified number of Shares, none of those Shares will be purchased. Hennessy will return all Shares tendered and not purchased pursuant to the Offer, including Shares not purchased because of proration or conditional tenders, to the tendering shareholders at Hennessy’s expense, promptly after the Expiration Date. See Sections 1, 3 and 5 of the Offer to Purchase.

The Offer is conditioned on a minimum of $1.0 million in aggregate value of Shares being tendered. The Offer is also subject to a number of other terms and conditions. See Section 7 of the Offer to Purchase.

Neil J. Hennessy, the Company’s Chairman of the Board, President and Chief Executive Officer, has advised Hennessy that he intends to tender 25% of the Shares that he beneficially owns, which is 471,630 Shares, in the Offer. Mr. Hennessy will not tender an amount of Shares beneficially owned by him that the Company’s outside legal counsel advises would be reasonably likely to result in a deemed change of control of the Company under the Investment Company Act of 1940, as amended, or the Investment Advisers Act of 1940, as amended. The Company’s remaining directors and executive officers have advised Hennessy that they intend to tender up to 25% of the Shares that they each beneficially own in the Offer. See Section 11 of the Offer to Purchase.

We are the owner of record of Shares held for your account. As such, we are the only ones who can tender your Shares, and then only pursuant to your instructions. WE ARE SENDING YOU THE LETTER OF TRANSMITTAL FOR YOUR INFORMATION ONLY; YOU CANNOT USE IT TO TENDER SHARES WE HOLD FOR YOUR ACCOUNT.

Please instruct us as to whether you wish us to tender any or all of the Shares we hold for your account on the terms and subject to the conditions of the Offer.

Please note the following:

| 1. | You may tender your Shares at a price of $25.00 per Share, as indicated in the attached Instruction Form, net to you in cash, less applicable withholding taxes and without interest.

| 2. | You should consult with your broker or other financial or tax advisors on the possibility of designating the priority in which your Shares will be purchased in the event of proration.

| 3. | The Offer, proration period and withdrawal rights will expire at 5:00 p.m., New York City time, on September 18, 2015 unless Hennessy extends or withdraws the Offer.

| 4. | The Offer is for up to $25.0 million in aggregate value of Shares. At the Purchase Price of $25.00 per Share, Hennessy could purchase 1,000,000 Shares if the Offer is fully subscribed, which would represent approximately 17% of Hennessy’s outstanding Shares as of August 19, 2015.

| 5. | Tendering shareholders who are tendering Shares held in their name or who tender their Shares directly to the Depositary will not be obligated to pay any brokerage commissions or fees to Hennessy or, except as set forth in the Offer to Purchase and the Letter of Transmittal, stock transfer taxes on Hennessy’s purchase of Shares under the Offer.

| 6. | If you are an odd lot holder and you instruct us to tender on your behalf all such Shares before the Expiration Date and check the box captioned “Odd Lots” on the attached Instruction Form, Hennessy will accept all such Shares for purchase before proration, if any, of the purchase of other Shares properly tendered and not properly withdrawn.

| 7. | If you wish to condition your tender upon the purchase of all Shares tendered or upon Hennessy’s purchase of a specified minimum number of the Shares that you tender, you may elect to do so and thereby avoid possible proration of your tender. If, based on the Purchase Price, it is necessary to permit Hennessy to purchase $25.0 million in aggregate value of Shares (or such greater amount as Hennessy may elect to pay, subject to applicable law), Hennessy will purchase Shares conditionally tendered (for which the condition was not initially satisfied) and not properly withdrawn, by random lot, to the extent feasible. To be eligible for purchase by random lot, shareholders whose Shares are conditionally tendered must have properly tendered and not properly withdrawn all of their Shares. To elect such a condition complete the box entitled “Conditional Tender” in the attached Instruction Form.

YOUR PROMPT ACTION IS REQUESTED. YOUR INSTRUCTION FORM SHOULD BE FORWARDED TO US IN AMPLE TIME TO PERMIT US TO SUBMIT A TENDER ON YOUR BEHALF BEFORE THE EXPIRATION DATE. PLEASE NOTE THAT THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS EXPIRE AT 5:00 P.M., NEW YORK CITY TIME, ON SEPTEMBER 18, 2015, UNLESS THE OFFER IS EXTENDED OR WITHDRAWN.

If you wish to have us tender any or all of your Shares, please so instruct us by completing, executing, detaching and returning to us the attached Instruction Form. If you authorize us to tender your Shares, we will tender all such Shares unless you specify otherwise on the attached Instruction Form.

The Offer is being made solely under the Offer to Purchase and the related Letter of Transmittal and is being made to all record holders of Shares of Hennessy. The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares of Hennessy residing in any state or other jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the securities, blue sky or other laws of such state or other jurisdiction.

INSTRUCTION FORM

The undersigned acknowledge(s) receipt of your letter and the enclosed Offer to Purchase, dated August 20, 2015 (the “Offer to Purchase”), and the related Letter of Transmittal (which together, as they may be amended and supplemented from time to time, constitute the “Offer”), in connection with the offer by Hennessy Advisors, Inc., a California corporation (“Hennessy” or the “Company”), to purchase for cash up to $25.0 million (but not less than $1.0 million) in aggregate value of the Common Stock, no par value per share (the “Shares”), by Hennessy at a price of $25.00 per Share, net to the seller in cash, less any applicable withholding taxes and without interest.

| 2 |

The undersigned hereby instruct(s) you to tender to Hennessy the number of Shares indicated below or, if no number is specified, all Shares you hold for the account of the undersigned, at the price per Share indicated below, upon the terms and subject to the conditions of the Offer.

Aggregate Number Of Shares To Be Tendered By You For The Account Of The Undersigned:

Shares.

| 3 |

ODD LOTS

(See Instruction 14 to the Letter of Transmittal)

To be completed ONLY if Shares are being tendered by or on behalf of a person owning, beneficially or of record, as of the close of business on the date set forth on the signature page hereto, and who continues to own, beneficially or of record, as of the Expiration Date, an aggregate of fewer than 100 Shares.

The undersigned either (check one box):

¨ | is the beneficial or record owner of an aggregate of fewer than 100 Shares, all of which are being tendered; or

¨ | is a broker, dealer, commercial bank, trust company, or other nominee that (a) is tendering for the beneficial owner(s), Shares with respect to which it is the record holder, and (b) believes, based upon representations made to it by the beneficial owner(s), that each such person is the beneficial owner of an aggregate of fewer than 100 Shares and is tendering all of the Shares beneficially owned by each such person.

CONDITIONAL TENDER

(See Instruction 13 to the Letter of Transmittal)

A shareholder may tender Shares subject to the condition that a specified minimum number of the shareholder’s Shares tendered pursuant to the Letter of Transmittal must be purchased if any Shares tendered are purchased, all as described in the Offer to Purchase, particularly in Section 6 thereof. Unless at least the minimum number of Shares indicated below is purchased by Hennessy pursuant to the terms of the Offer, none of the Shares tendered will be purchased. It is the tendering shareholder’s responsibility to calculate that minimum number of Shares that must be purchased if any are purchased, and Hennessy urges shareholders to read carefully Section 13 of the Offer to Purchase and consult their own tax advisors before completing this section. Unless this box has been checked and a minimum specified, the tender will be deemed unconditional.

¨ | The minimum number of Shares that must be purchased, if any are purchased, is: Shares.

If, because of proration, the minimum number of Shares designated will not be purchased, Hennessy may accept conditional tenders by random lot, if necessary. However, to be eligible for purchase by random lot, the tendering shareholder must have tendered all of his or her Shares and checked this box:

¨ | The tendered Shares represent all Shares held by the undersigned.

The method of delivery of this document is at the election and risk of the tendering shareholder. If delivery is by mail, then registered mail with return receipt requested, properly insured, is recommended. In all cases, sufficient time should be allowed to ensure timely delivery.

The Board of Directors of the Company has approved the Offer. However, none of the Company, any employee of the Company, any member of the Board of Directors of the Company, the Information Agent or the Depositary makes any recommendation to shareholders as to whether they should tender or refrain from tendering their Shares.

None of the Company, any employee of the Company, any member of the Board of Directors of the Company, the Information Agent or the Depositary has authorized any person to make any recommendation with respect to the Offer. Shareholders should carefully evaluate all information in the Offer to Purchase, consult their own financial and tax advisors and make their own decisions about whether to tender Shares and, if so, how many Shares to tender.

| 4 |

SIGNATURE

Signature(s): __________________________________________________________________________________
Name(s): _____________________________________________________________________________________
(Please Print)
Taxpayer Identification or Social Security Number: ___________________________________________________
Address(es): __________________________________________________________________________________
(Including Zip Code)
Phone Number (including Area Code): ____________________________________________________________
Date: _______________________________________________________________________________________

| 5 |