Exhibit 10.5

GRAF ACQUISITION CORP. IV

1790 Hughes Landing Blvd., Suite 400

The Woodlands, Texas 77380

May 20, 2021

G-SPAC Management LLC 

1790 Hughes Landing Blvd., Suite 400 

The Woodlands, Texas 77380

Re: Administrative Services Agreement

Ladies and Gentlemen:

This letter agreement (this “Agreement”) by and among Graf Acquisition Corp. IV (the “Company”) and G-SPAC Management LLC (the “Sponsor”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on the New York Stock Exchange (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

1.       The Sponsor shall make available, or cause to be made available, to the Company, at 1790 Hughes Landing Blvd., Suite 400, The Woodlands, Texas 77380 (or any successor location) and elsewhere, office space and secretarial and administrative services as may be reasonably required by the Company. In exchange therefor, the Company shall pay the Sponsor $15,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date; and

2.       The Sponsor hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this Agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public stockholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, this Agreement, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

This Agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

No party hereto may assign either this Agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This Agreement constitutes the entire relationship of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York.

[Signature Page Follows]

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Very truly yours,
GRAF ACQUISITION CORP. IV
By:	/s/ James A. Graf
Name: James A. Graf
Title: Chief Executive Officer

AGREED AND ACCEPTED BY:
G-SPAC MANAGEMENT, LLC
By:	/s/ James A. Graf
	Name: James A. Graf
	Title: Manager

[Signature Page to Administrative Services Agreement]