EX-10.5




 Exhibit 10.5 

Spindletop Health Acquisition Corp. 

3571 Far West Blvd., Suite 108 

Austin, TX 78731 

November 3, 2021 
 Spindletop Capital
Management, LLC 
 3571 Far West Blvd., Suite 108 
 Austin, TX
78731 
 Re: Administrative Services Agreement 

Gentlemen: 
 This letter will confirm our
agreement that, commencing on the date the securities of Spindletop Health Acquisition Corp. (the “Company”) are first listed on the Nasdaq Global Market (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the 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”), Spindletop Capital Management, LLC
(“Management”) shall make available to the Company, at 3571 Far West Blvd., Suite 108 Austin, TX 78731 (or any successor location), certain office space, utilities, and general office, receptionist and secretarial support and other
administrative services as may be reasonably required by the Company. In exchange therefor, the Company shall pay Management the sum of $20,000 per month on the Listing Date and continuing monthly thereafter and will be entitled to be
reimbursed for any out-of-pocket expenses until the Termination Date. 

Management hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind (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 letter 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 letter agreement may not be amended, modified or waived as to any particular provision, except by
a written instrument executed by all parties hereto. 
 No party hereto may assign either this letter 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. 
 [Signature page follows] 











 This letter agreement, 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, without giving effect to its choice of laws
principles. 
  

			
	Very truly yours,
	
	SPINDLETOP HEALTH ACQUISITION CORP.
		
	By:	 	 /s/ Evan Melrose

		 	Name: Dr. Evan Melrose
		 	Title: Chief Executive Officer


 AGREED TO AND ACCEPTED BY: 

SPINDLETOP CAPITAL MANAGEMENT, LLC 
  

			
	By:	 	 /s/ Evan Melrose

		 	Name: Dr. Evan Melrose
		 	Title: Managing Member

 [Signature Page to Administrative Services Agreement]