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Exhibit 10.5.1

FIRST AMENDMENT
TO
AMENDED AND RESTATED STOCKHOLDERS' AGREEMENT

THIS FIRST AMENDMENT TO AMENDED AND RESTATED STOCKHOLDERS' AGREEMENT (this "Amendment") is made and entered into effective April 8, 1999, by and among PROS Strategic Solutions, Inc., a Delaware corporation (the "Company"), and the undersigned holders of a majority of the total number of shares of Common Stock held by the Investors, the Founding Stockholders and the Stockholders. Capitalized terms used and not defined herein have the same meaning ascribed to them in the Agreement (as hereinafter defined).

W I T N E S S E T H:

WHEREAS, the Company, the Investors, the Founding Stockholders, and the Stockholders entered into that certain Amended and Restated Stockholders' Agreement dated effective June 8, 1998 (the "Agreement");

WHEREAS, Section 4.6 of the Agreement provides that the Agreement may be amended from time to time by an instrument in writing signed by the Company and the holders of a majority of the total number of shares of Common Stock held by the Investors, the Founding Stockholders, and the Stockholders, provided, however, that no amendment shall impose any additional material obligation on the Investors, the Founding Stockholders or any Stockholder without that party's written consent to such amendment;

WHEREAS, the parties to this Amendment (other than the Company) are the holders of a majority of the total number of shares of Common Stock held by the Investors, the Founding Stockholders, and the Stockholders; and

WHEREAS, the parties to this Amendment wish to amend the Agreement as hereinafter provided;

NOW, THEREFORE, in consideration of the premises and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. The Agreement is hereby amended to add a new Section 4.16 which reads in its entirety as follows:

"4.16 "Termination of Employee Stockholder's Rights and Obligations." Notwithstanding anything contained in this Agreement to the contrary, if an Employee Stockholder shall for any reason cease to be an officer or employee of the Company, the rights and obligations of the parties hereto under this Agreement with respect to such Employee Stockholder and the shares of Common Stock owned or acquired by such Employee Stockholder may (but shall not be required to) be terminated, in whole or in part, by an instrument in writing signed by the Company, such Employee Stockholder and the holders of a majority of the total number of shares of Common Stock held by the Investors, the Founding Stockholders and the Stockholders."

2. All references to "this Agreement" contained in the Agreement shall be deemed to be a reference to the Agreement, as amended by this Amendment.

3. This Amendment shall be subject to and governed by the laws of the State of Delaware.

4. Except as amended by this Amendment, the Agreement shall remain in full force and effect.

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5. This Amendment may be executed in one or more counterparts, and by the different parties hereto in separate counterparts, each of which when executed shall be deemed to be an original but all of which shall constitute one and the same agreement.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be executed effective as of the date first above written.

|  | PROS STRATEGIC SOLUTIONS, INC.
|  | By |  | /s/ CHARLES H. MURPHY Charles H. Murphy Chief Financial Officer
|  | FOUNDING STOCKHOLDERS:
|  | /s/ RONALD F. WOESTEMEYER Ronald F. Woestemeyer
|  | /s/ MARIETTE MELCHIOR WOESTEMEYER Mariette Melchior Woestemeyer

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|  | INVESTORS:
|  | TA/Advent VIII L.P.
|  | By: |  | TA Associates VIII LLC, its General Partner
|  | By: |  | TA Associates, Inc., its Manager
|  | By |  | /s/ KURT R. JAGGERS Kurt R. Jaggers Attorney-in-Fact

[SIGNATURES CONTINUED ON NEXT PAGE]

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|  | ADVENT ATLANTIC AND PACIFIC III, L.P.
|  | By: |  | TA Associates AAP III Partners, Its General Partner
|  | By: |  | TA Associates, Inc.
|  | By |  | /s/ KURT R. JAGGERS Kurt R. Jaggers Attorney-in-Fact
|  | TA VENTURE INVESTORS, L.P.
|  | By |  | /s/ KURT R. JAGGERS Kurt R. Jaggers Attorney-in-Fact
|  | TA EXECUTIVE FUND LLC
|  | By: |  | TA Associates VIII LLC, its General Partner
|  | By: |  | TA Associates, Inc., its Manager
|  | By |  | /s/ KURT R. JAGGERS Kurt R. Jaggers Attorney-in-Fact
|  | JMI EQUITY FUND III, L.P.
|  | By: |  | JMI Associates III, LLC, its General Partner
|  | By |  | /s/ HARRY S. GRUNER Harry S. Gruner Managing Member
|  | /s/ WILLIAM H. WOLF William H. Wolf

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CONSENT

We, David Samuel Coats and wife, Judy Coats, hereby affirm and attest by our signatures to this Consent that we have read that certain First Amendment to Amended and Restated Stockholders' Agreement dated as of April 8, 1999 (the "Amendment"), a copy of which is attached hereto as Exhibit A, and that we are fully aware of, understand, and fully consent and agree to the terms and provisions of the Amendment.

Date: |  |  |  |  |  | David Samuel Coats
|  |  |  |  |  | Judy Coats

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FIRST AMENDMENT TO AMENDED AND RESTATED STOCKHOLDERS' AGREEMENT
W I T N E S S E T H
CONSENT