Document:

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]Exhibit 10.5

 

PRIVATE PLACEMENT 

WARRANTS PURCHASE AGREEMENT

 

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT,
dated as of January 14, 2021 (this “Agreement”), is entered into by and between Hennessy Capital Investment
Corp. V, a Delaware corporation (the “Company”), and Hennessy Capital Partners V LLC, a Delaware limited liability
company (the “Purchaser”).

 

WHEREAS, the Company intends to consummate
an initial public offering of the Company’s units (the “Public Offering”), each unit consisting of one
share of the Company’s Class A common stock, par value $0.0001 per share (a “Share”), and one-fourth
of one redeemable warrant, each whole warrant exercisable for one Share at an exercise price of $11.50 per Share, as set forth
in the Company’s registration statement on Form S-1 related to the Public Offering (the “Registration Statement”);
and

 

WHEREAS, the Purchaser now wishes to purchase
an aggregate of 4,433,333 warrants (or 4,853,333 warrants if the underwriters’ over-allotment option is exercised in full)
(the “Warrants”), each Warrant entitling the holder to purchase one Share at an exercise price of $11.50 per
Share.

 

NOW THEREFORE, in consideration of the mutual
promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows:

 

AGREEMENT

 

Section 1. Authorization, Purchase
and Sale; Terms of the Warrants.

 

A. Authorization of the
Warrants. The Company has duly authorized the issuance and sale of the Warrants to the Purchaser.

 

B. Purchase and Sale of
the Warrants.

 

(i) As payment in full for
the 4,433,333 Warrants being purchased under this Agreement, the Purchaser shall pay $6,650,000 (the “Purchase Price”),
by wire transfer of immediately available funds in accordance with the Company’s wiring instructions, at least one (1) business
day prior to the effective date of the Registration Statement, or on such other date as the Company and the Purchaser may agree.

 

(ii) In the event that the
underwriters’ over-allotment option is exercised in full, the Purchaser shall purchase up to an additional 420,000 Warrants
(the “Additional Warrants”), in the same proportion as the amount of the over-allotment option that is exercised,
and simultaneously with such purchase of Additional Warrants, as payment in full for the Additional Warrants being purchased hereunder,
and at least one (1) business day prior to the closing of all or any portion of the over-allotment option, or on such other
date as the Company and the Purchaser may agree, the Purchaser shall pay $1.50 per Additional Warrant, up to an aggregate
amount of $630,000, by wire transfer of immediately available funds in accordance with the Company’s wiring instructions.

 

(iii) The closing of the purchase
and sale of the Warrants shall take place simultaneously with the closing of the Public Offering (the “Initial Closing
Date”). The closing of the purchase and sale of the Additional Warrants, if applicable, shall take place simultaneously
with the closing of all or any portion of the over-allotment option (such closing date, together with the Initial Closing Date,
the “Closing Dates” and each, a “Closing Date”). The closing of the purchase and sale of
each of the Warrants and the Additional Warrants shall take place at the offices of Ellenoff Grossman & Schole LLP, 1345 Avenue
of the Americas, New York, New York 10105, or such other place as may be agreed upon by the parties hereto.

 

     

     

    

 

C. Terms of the Warrants.

 

(i) The Warrants shall have
their terms set forth in a Warrant Agreement to be entered into by the Company and a warrant agent, in connection with the Public
Offering (a “Warrant Agreement”).

 

(ii) At or prior to the time
of the Initial Closing Date, the Company and the Purchaser shall enter into a registration rights agreement (the “Registration
Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to
the Warrants and the Shares underlying the Warrants.

 

Section 2. Representations and Warranties
of the Company. As a material inducement to the Purchaser to enter into this Agreement and purchase the Warrants, the Company
hereby represents and warrants to the Purchaser (which representations and warranties shall survive the Closing Dates) that:

 

A. Organization and Corporate
Power. The Company is a corporation duly organized, validly existing and in good standing under the laws of the State of Delaware
and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a
material adverse effect on the financial condition, operating results or assets of the Company. The Company possesses all requisite
corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement.

 

B. Authorization; No Breach.

 

(i) The execution, delivery
and performance of this Agreement and the Warrants have been duly authorized by the Company as of the Closing Dates. This Agreement
constitutes a valid and binding obligation of the Company, enforceable in accordance with its terms. Upon issuance in accordance
with, and payment pursuant to, the terms of the Warrant Agreement and this Agreement, the Warrants will constitute valid and
binding obligations of the Company, enforceable in accordance with their terms as of the Closing Dates.

 

(ii) The execution and delivery
by the Company of this Agreement and the Warrants, the issuance and sale of the Warrants, the issuance of the Shares upon exercise
of the Warrants and the fulfillment of, and compliance with, the respective terms hereof and thereof by the Company, do not and
will not as of the Closing Dates (a) conflict with or result in a breach of the terms, conditions or provisions of, (b) constitute
a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s
capital stock or assets under, (d) result in a violation of, or (e) require any authorization, consent, approval, exemption
or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency pursuant
to the certificate of incorporation or the bylaws of the Company (in effect on the date hereof or as may be amended prior to completion
of the contemplated Public Offering), or any material law, statute, rule or regulation to which the Company is subject, or
any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof
under federal or state securities laws.

 

C. Title to Securities.
Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the Shares issuable upon
exercise of the Warrants will be duly and validly issued, fully paid and nonassessable. Upon issuance in accordance with, and payment
pursuant to, the terms hereof and the Warrant Agreement, the Purchaser will have good title to the Warrants and the Shares issuable
upon exercise of such Warrants, free and clear of all liens, claims and encumbrances of any kind, other than (i) transfer
restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal and state
securities laws, and (iii) liens, claims or encumbrances imposed due to the actions of the Purchaser.

 

D. Governmental Consents.
No permit, consent, approval or authorization of, or declaration to or filing with, any governmental authority is required in connection
with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other transactions
contemplated hereby.

 

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E. Regulation D Qualification.
Neither the Company nor, to its knowledge, any of its affiliates, officers, directors or beneficial stockholders of 20% or more
of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation
D under the Securities Act of 1933, as amended (the “Securities Act”).

 

Section 3. Representations and Warranties
of the Purchaser. As a material inducement to the Company to enter into this Agreement and issue and sell the Warrants to the
Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive
the Closing Dates) that:

 

A. Organization and Requisite
Authority. The Purchaser possesses all requisite power and authority necessary to carry out the transactions contemplated by
this Agreement.

 

B. Authorization; No Breach.

 

(i) This Agreement constitutes
a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent
conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights
and to general equitable principles (whether considered in a proceeding in equity or law).

 

(ii) The execution and delivery
by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser does not and shall
not as of the Closing Dates conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of any
agreement, instrument, order, judgment or decree to which the Purchaser is subject.

 

C. Investment Representations.

 

(i) The Purchaser is acquiring
the Warrants and, upon exercise of the Warrants, the Shares issuable upon such exercise (collectively, the “Securities”),
for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with,
any public sale or distribution thereof.

 

(ii) The Purchaser is an “accredited
investor” as such term is defined in Rule 501(a)(3) of Regulation D under the Securities Act and the Purchaser
has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities
Act.

 

(iii) The Purchaser understands
that the Securities are being offered and will be sold to it in reliance on specific exemptions from the registration requirements
of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the
Purchaser’s compliance with, the representations and warranties of the Purchaser set forth herein in order to determine the
availability of such exemptions and the eligibility of the Purchaser to acquire such Securities.

 

(iv) The Purchaser did not
enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under
the Securities Act.

 

(v) The Purchaser has been
furnished with all materials relating to the business, finances and operations of the Company and materials relating to the offer
and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions
of the executive officers and directors of the Company. The Purchaser understands that its investment in the Securities involves
a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed
investment decision with respect to the acquisition of the Securities.

 

(vi) The Purchaser understands
that no United States federal or state agency or any other government or governmental agency has passed on or made any recommendation
or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such
authorities passed upon or endorsed the merits of the offering of the Securities.

 

    3

     

    

 

(vii) The Purchaser understands
that: (a) the Securities have not been and are not being registered under the Securities Act or any state securities laws,
and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold
in reliance on an exemption therefrom; and (b) except as specifically set forth in the Registration Rights Agreement, neither
the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities
laws or to comply with the terms and conditions of any exemption thereunder.

 

(viii) The Purchaser has such
knowledge and experience in financial and business matters, knowledge of the high degree of risk associated with investments in
the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment
in the Securities and is able to bear the economic risk of an investment in the Securities in the amount contemplated hereunder
for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies
and will have no current or anticipated future needs for liquidity which would be jeopardized by the investment in the Securities.
The Purchaser can afford a complete loss of its investments in the Securities.

 

Section 4. Conditions of the Purchaser’s
Obligations. The obligations of the Purchaser to purchase and pay for the Warrants are subject to the fulfillment, on or before
the Closing Dates, of each of the following conditions:

 

A. Representations and
Warranties. The representations and warranties of the Company contained in Section 2 shall be true and correct
at and as of the Closing Dates as though then made.

 

B. Performance. The
Company shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before the Closing Dates.

 

C. No Injunction.
No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated
or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority
over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement
or the Warrant Agreement.

 

D. Warrant Agreement.
The Company shall have entered into a Warrant Agreement with a warrant agent on terms satisfactory to the Purchaser (the “Warrant
Agreement”).

 

Section 5. Conditions of the Company’s
Obligations. The obligations of the Company to the Purchaser under this Agreement are subject to the fulfillment, on or before
the Closing Dates, of each of the following conditions:

 

A. Representations and
Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be true
and correct at and as of the Closing Dates as though then made.

 

B. Performance. The
Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by the Purchaser on or before the Closing Dates.

 

C. No Injunction.
No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated
or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority
over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement
or the Warrant Agreement.

 

D. Warrant Agreement.
The Company shall have entered into the Warrant Agreement.

 

    4

     

    

 

Section 6. Termination. This Agreement
may be terminated at any time after June 30, 2021 upon the election by either the Company or a Purchaser entitled to purchase a
majority of the Warrants upon written notice to the other parties if the closing of the Public Offering does not occur prior to
such date.

 

Section 7. Survival of Representations
and Warranties. All of the representations and warranties contained herein shall survive the Closing Dates.

 

Section 8. Definitions. Terms used
but not otherwise defined in this Agreement shall have the meaning assigned to such terms in the Registration Statement.

 

Section 9.  Miscellaneous.

 

A. Successors and Assigns.
Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or on behalf of any
of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed
or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign this Agreement, other than
assignments by the Purchaser to affiliates thereof.

 

B. Severability. Whenever
possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law,
but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective
only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

 

C. Counterparts. This
Agreement may be executed simultaneously in two or more counterparts, none of which need contain the signatures of more than one
party, but all such counterparts taken together shall constitute one and the same agreement.

 

D. Descriptive Headings;
Interpretation. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive
part of this Agreement. The use of the word “including” in this Agreement shall be by way of example rather than by
limitation.

 

E. Governing Law.
This Agreement and the rights and obligations of the parties hereunder shall be construed in accordance with and governed by the
laws of New York applicable to contracts wholly performed within the borders of such state, without giving effect to the conflict
of law principles thereof. The parties hereto irrevocably submit to the exclusive jurisdiction of any federal court sitting in
the Southern District of New York or any state court located in New York County, State of New York, over any suit, action or proceeding
arising out of or relating to this Agreement. To the fullest extent they may effectively do so under applicable law, the parties
hereto irrevocably waive and agree not to assert, by way of motion, as a defense or otherwise, any claim that they are not subject
to the jurisdiction of any such court, any objection that they may now or hereafter have to the laying of the venue of any such
suit, action or proceeding brought in any such court and any claim that any such suit, action or proceeding brought in any such
court has been brought in an inconvenient forum.

 

F. Amendments. 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.

 

[Signature page follows]

 

    5

     

    

 

IN WITNESS WHEREOF, the parties hereto
have executed this Agreement to be effective as of the date first set forth above.

 

	 	COMPANY:
	 	 
	 	HENNESSY CAPITAL INVESTMENT CORP. V
	 	 	 
	 	By:	/s/ Daniel J. Hennessy
	 	 	Name: Daniel J. Hennessy
	 	 	Title:  Chief Executive Officer

 

	 	HENNESSY CAPITAL PARTNERS V LLC
	 	 	 
	 	By:	/s/ Daniel J. Hennessy
	 	 	Name: Daniel J. Hennessy
	 	 	Title:  Managing Member

 

[Signature Page to Private Placement
Warrants Purchase Agreement]

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