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]




    2 


     


    

	 	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]