Exhibit 5.1

JONES DAY

SILICON VALLEY OFFICE • 1755 EMBARCADERO ROAD • PALO ALTO, CALIFORNIA 94303

TELEPHONE: +1.650.739.3939 • FACSIMILE: +1.650.739.3900

March 24, 2014

Five9, Inc.

Bishop Ranch 8

4000 Executive Parkway, Suite 400

San Ramon, California 94583

| Re: | Registration Statement on Form S-1, as amended (No. 333-194258)

Relating to the Initial Public Offering of up to

11,500,000 shares of Common Stock of Five9, Inc.

Ladies and Gentlemen:

We are acting as counsel for Five9, Inc., a Delaware corporation (the “Company”), in connection with the initial public offering and sale by the Company of up to 11,500,000 shares (the “Shares”) of common stock, par value $0.001 per share, pursuant to the Underwriting Agreement (the “Underwriting Agreement”) proposed to be entered into by and among the Company and J.P. Morgan Securities LLC and Barclays Capital Inc., acting as the representatives of the several underwriters to be named in Schedule 1 thereto.

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinion. Based upon the foregoing and subject to the further assumptions, qualifications and limitations set forth herein, we are of the opinion that the Shares, when issued and delivered pursuant to the Underwriting Agreement against payment of the consideration therefor as provided in the Underwriting Agreement, will be validly issued, fully paid and nonassessable.

In rendering the foregoing opinion, we have assumed that the Company will issue and deliver the Shares after filing with the Secretary of State of the State of Delaware (i) the Certificates of Amendment to the Company’s Amended and Restated Certificate of Incorporation, in the form approved by us and filed as an exhibit to the Registration Statement (as defined below) and (ii) the Company’s Amended and Restated Certificate of Incorporation to be in effect upon completion of the initial public offering, in the form approved by us and filed as an exhibit to the Registration Statement.

The opinion expressed herein is limited to the General Corporation Law of the State of Delaware, and we express no opinion as to the effect of the laws of any other jurisdiction.

ALKHOBAR • ATLANTA • BEIJING • BOSTON • BRUSSELS • CHICAGO • CLEVELAND • COLUMBUS • DALLAS • DUBAI

DÜSSELDORF • FRANKFURT • HONG KONG • HOUSTON • IRVINE • JEDDAH • LONDON • LOS ANGELES • MADRID

MEXICO CITY • MILAN • MOSCOW • MUNICH • NEW YORK · PARIS • PITTSBURGH · RIYADH · SAN DIEGO

SAN FRANCISCO • SÃO PAULO · SHANGHAI • SILICON VALLEY · SINGAPORE • SYDNEY • TAIPEI • TOKYO • WASHINGTON

Five9, Inc. Page 2 |  | JONES DAY

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement on Form S-1, as amended (No. 333-194258) (the “Registration Statement”), filed by the Company to effect registration of the Shares under the Securities Act of 1933 (the “Act”) and to the reference to us under the caption “Legal Matters” in the prospectus constituting a part of such Registration Statement. In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day