Exhibit 10.5


Crypto 1 Acquisition Corp


1221 Brickell Avenue


Miami, Florida 33131


December 6, 2021


Crypto 1 Sponsor LLC


1221 Brickell Avenue


Miami, Florida 33131


 


Ladies and Gentlemen:


 


This letter will confirm our agreement that, commencing on the date
(the “Effective Date”) that the securities of Crypto 1 Acquisition Corp (the “Company”)
are first listed on the Nasdaq Capital Market 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 on Form S-1 (File No. 333-261051)
filed with the Securities and Exchange Commission for the initial public offering (the “IPO”) of the Company’s
securities) (such earlier date hereinafter referred to as the “Termination Date”), Crypto 1 Sponsor LLC or an
affiliate of Crypto 1 Sponsor LLC (the “Provider”) shall take steps directly or indirectly to make available,
or cause to be made available, to the Company certain office space, secretarial and administrative services as may be reasonably required
by the Company from time to time, situated at 1221 Brickell Avenue, Miami, Florida 33131 (or any successor location of the Provider).
In exchange therefor, the Company shall pay the Provider a sum of $10,000 per month on the Effective Date and continuing monthly thereafter
on the first day of each month until the Termination Date.


 


The Provider hereby (i) 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 established
for the benefit of the public shareholders of the Company and into which substantially all of the proceeds of the Company’s IPO
will be deposited (the “Trust Account”), (ii) irrevocably waives any Claim it presently has or may have in the
future as a result of, or arising out of, this letter agreement, which Claim would reduce, encumber, or otherwise adversely affect the
Trust Account or any monies or other assets in the Trust Account and (iii) agrees that it will not seek recourse against the Trust Account
or any monies or other assets in the Trust Account for any reason whatsoever.


 


The Provider (on behalf of itself and its affiliates) grants, and shall
cause its affiliates to grant, to the Company a non-exclusive, fully paid-up, royalty-free, non-sublicensable and non-transferable limited
license, until the Termination Date, to use and exploit the “Crypto 1” word mark and the Crypto 1 logo solely in connection
with the business of the Company and to hold itself out as “Crypto 1 Acquisition Corp”. Any goodwill accruing from the Company’s
use of the licensed trademarks will inure solely to the Provider and its affiliates.


 






    


     


    

 


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 hereto may not assign this letter agreement and any of
their rights, interests, or obligations hereunder without the consent of the other party; provided that the Provider may assign
this letter agreement to an affiliate without the prior written approval of the Company.


 


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. In the event that any signature is delivered by facsimile transmission or any other form of electronic delivery,
such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with
the same force and effect as if such signature page were an original thereof.


 






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	 	Sincerely,
	 	 	 
	 	CRYPTO 1 ACQUISITION CORP
	 	 	 
	 	By:	/s/ Michael (Xu) Zhao
	 	Name:	Michael (Xu) Zhao
	 	Title: 	Chief Executive Officer



 


	AGREED AND ACCEPTED BY:	 
	 	 	 
	CRYPTO 1 SPONSOR LLC	 
	 	 	 
	By:	/s/ David Hytha	 
	Name:	David Hytha	 
	Title: 	Managing Member	 



 


[Signature Page to Administrative Services Agreement]