Exhibit 10.4


 


HENNESSY CAPITAL INVESTMENT CORP. V


3415 N. Pines Way, Suite 204


Wilson, Wyoming 83014


 


January 14, 2021


 


Hennessy Capital LLC


3415 N. Pines Way, Suite 204


Wilson, Wyoming 83014


 


Re: Administrative Support Agreement


 


Ladies and Gentlemen:


 


This letter agreement
by and between Hennessy Capital Investment Corp. V (the “Company”) and Hennessy Capital LLC (“Hennessy
Capital”), 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 Nasdaq Capital Market (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”):


 


(i) Hennessy Capital
shall make available, or cause to be made available, to the Company, at 3415 N. Pines Way, Suite 204, Wilson, Wyoming 83014 (or
any successor location of Hennessy Capital), certain office space, utilities and secretarial and administrative support as may
be reasonably required by the Company. In exchange therefor, the Company shall pay Hennessy Capital the sum of $15,000 per month
on the Listing Date and continuing monthly thereafter until the Termination Date; and


 


(ii) Hennessy
Capital 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 letter 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”)
as a result of, or arising out of, this letter agreement, and hereby irrevocably waives any Claim it may have in the future, 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 the 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.


 


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


 


[Signature Page Follows]


 




     


     


    

 


	 	Very truly yours,
	 	 
	 	HENNESSY CAPITAL INVESTMENT CORP. V
	 	 	 
	 	By:	/s/ Daniel J. Hennessy
	 	 	Name: 	Daniel J. Hennessy
	 	 	Title: 	Chief Executive Officer


 


	AGREED TO AND ACCEPTED BY:	 
	 	 
	HENNESSY CAPITAL LLC	 
	 	 
	By:	/s/ Daniel J. Hennessy	 
	Name: 	Daniel J. Hennessy	 
	Title:	Managing Member	 


 


[Signature Page to Administrative Support
Agreement]