Exhibit 10.5

      

      

      PROOF Acquisition Corp I

      11911 Freedom Drive, Suite 1080

      Reston, VA 20190

      

      

      November 30, 2021

      

      

      PROOF Acquisition Sponsor I, LLC

      11911 Freedom Drive, Suite 1080

      Reston, VA 20190

      

      

      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 PROOF Acquisition Corp I (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”), PROOF Acquisition Sponsor I, 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 11911 Freedom Drive, Suite 1080, Reston, VA
        20190 (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.

      

      

      [Signature Page Follows]

      

      

      
        
          


      

      

      

      	 	
              Very truly yours,

            
	 	 	 
	 	
              PROOF ACQUISITION CORP I

            
	 	 	 
	 	
              By:

            	/s/ John C. Backus, Jr.

            
	 	 	
              Name: John C. Backus, Jr.

            
	 	 	
              Title: Chief Executive Officer and Director

              

            


      

      

      

      

      	
              AGREED TO AND ACCEPTED BY:

            	 
	 	 	 
	
              PROOF ACQUISITION SPONSOR I, LLC

            	 
	By:

            	
              PROOF Sponsor Management, LLC 

              

              Its Manager

              

            	 
	 	 	 
	
              By:

            	/s/ Steven P. Mullins

            	 
	 	
              Name: Steven P. Mullins

            	 
	 	
              Title: Managing Member

              

            	 


      

      

      

      

      

      

      [Signature Page to Administrative Services Agreement]