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                                                                    Exhibit 10.5

                      TEXAS GENCO SHORT TERM INCENTIVE PLAN
                        (Effective as of January 1, 2004)

                                 First Amendment

            Texas Genco Holdings, Inc., a Texas corporation, having established
the Texas Genco Short Term Incentive Plan, effective as of January 1, 2004 (the
"Plan"), and having reserved the right under Section 13 thereof to amend the
Plan, does hereby amend the Plan, effective as of October 1, 2004, to read as
follows:

            1. The Plan is hereby amended to provide that, except as provided in
Paragraph 3 herein, all references to "Texas Genco Holdings, Inc." are hereby
deleted and replaced in lieu thereof with "Texas Genco, LP" and the definition
of "Company" in Section 2 of the Plan is hereby amended to read as follows:

            "COMPANY: Texas Genco, LP, a Texas limited partnership, or its
successors."

            2. Section 2 of the Plan is hereby amended to add the following new
definitions thereto:

            "GENERAL PARTNER: The general partner of the Company.

            SCHEDULED EMPLOYEE: An Employee who is a Scheduled Employee on
      Section 6.8(a) of the Companies Disclosure Letter as defined in Section
      4.3(a) of the Transaction Agreement.

            TRANSACTION AGREEMENT: That certain Transaction Agreement among
      CenterPoint Energy, Inc., Utility Holding, LLC, NN Houston Sub, Inc.,
      Texas Genco Holdings, Inc., HPC Merger Sub, Inc. and GC Power Acquisition
      LLC, dated as of July 21, 2004."

            3. The definitions of "Committee," "Employee" and "Subsidiary" in
Section 2 of the Plan are hereby amended to read as follows:

            "COMMITTEE: The Compensation Committee of the Board of Directors of
      the General Partner.

            EMPLOYEE: An employee of the Company or any of its Subsidiaries, or
      a Scheduled Employee who, immediately prior to the -------- execution date
      of the Transaction Agreement, was a Participant in the Plan.

            SUBSIDIARY: A subsidiary corporation with respect to the Company as
      defined in Section 424(f) of the Code; provided, however, that, the
      foregoing

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      notwithstanding, for purposes of this Plan, Texas Genco Holdings, Inc. and
      its direct and indirect affiliates and subsidiaries shall be deemed to be
      Subsidiaries during the period commencing on the `Non-STP Acquisition
      Closing Date' under the Transaction Agreement and ending on the `STP
      Acquisition Closing Date' under the Transaction Agreement."

            4. Section 2 of the Plan is hereby amended to delete the definition
of "Board of Directors or Board" and, except as provided in the definition of
"Committee" in Paragraph 2 herein, all references in the Plan to "Board of
Directors" or "Board" are hereby deleted and replaced in lieu thereof with
"General Partner."

            IN WITNESS WHEREOF, Texas Genco Holdings, Inc. and Texas Genco, LP,
have caused these presents to be executed by their duly authorized officers in a
number of copies, all of which shall constitute one and the same instrument,
which may be sufficiently evidenced by any executed copy hereof, on this 22nd
day of September, 2004, but effective as of the date specified herein.

                                       TEXAS GENCO HOLDINGS, INC.

                                       By /s/ DAVID G. TEES
                                          --------------------------------------
                                          David G. Tees
                                          Chief Executive Officer
ATTEST:

/s/ RICHARD DAUPHIN
--------------------------

                                       TEXAS GENCO, LP

                                       BY:  TEXAS GENCO GP, LLC
                                       ITS GENERAL PARTNER

                                       By /s/ DAVID G. TEES
                                          --------------------------------------
                                          David G. Tees
                                          President and Chief Executive Officer

ATTEST:

/s/ RICHARD DAUPHIN
--------------------------

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