EX-10.5





 Exhibit 10.5 

H.I.G. ACQUISITION CORP. 

1450 Brickell Avenue 
 31st Floor

 Miami, FL 33131 
 October 23,
2020 
 H.I.G. Acquisition Advisors, LLC. 
 1450 Brickell
Avenue 
 31st Floor 
 Miami, FL 33131 

Ladies and Gentlemen: 
 This letter will confirm
our agreement that, commencing on the effective date (the “Effective Date”) of the registration statement (the “Registration Statement”) for the initial public offering (the
“IPO”) of the securities of H.I.G. Acquisition Corp. (the “Company”) and continuing until the earlier of (i) the consummation by the Company of an initial business combination and (ii) the
Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”), H.I.G. Acquisition Advisors, LLC (the
“Sponsor”) shall take steps directly or indirectly to make available to the Company certain office space, secretarial and administrative services as may be required by the Company from time to time, situated at 1450 Brickell
Avenue, 31st Floor, Miami, FL 33131 (or any successor location). In exchange therefore, the Company shall pay the Sponsor a sum of $10,000 per month on the Effective Date and continuing monthly thereafter until the Termination Date. The Sponsor
hereby agrees that it does not have any right, title, interest or claim of any kind (a “Claim”) in or to any monies that may be set aside in a trust account (the “Trust Account”) that may be
established upon the consummation of the IPO and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, any negotiations, contracts or agreements with the Company and will not seek recourse against 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 the parties hereto. 
 The parties may not assign this letter agreement and any of their rights, interests, or obligations
hereunder without the consent of the other party. 
 This letter agreement 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 that will apply the laws of another jurisdiction. 

This letter agreement may be executed in one or more counterparts, each of which shall for all purposes be deemed to be an original but all of
which together shall constitute one and the same agreement. Only one such counterpart signed by the party against whom enforceability is sought needs to be produced to evidence the existence of this letter agreement. 

 

  
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	Very truly yours,
	
	H.I.G. ACQUISITION CORP.
		
	By:	 	 /s/ Brian Schwartz

	Name:	 	Brian Schwartz
	Title:	 	Chief Executive Officer


  

			
	AGREED TO AND ACCEPTED BY:
	
	H.I.G. ACQUISITION ADVISORS, LLC
		
	By:	 	 /s/ Brian Schwartz

	Name:	 	Brian Schwartz
	Title:	 	Chief Executive Officer


  
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Administrative Services Agreement]