EX-10.5





 Exhibit 10.5 

PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT 

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT (as it may from time to time be amended, this “Agreement”), dated as of
October 4, 2021, is entered into by and among Crixus BH3 Acquisition Company, a Delaware corporation (the “Company”), and Crixus BH3 Sponsor, 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 Class A common stock of the Company, par value $0.0001 per share (each, a “Share”), and one-half of one redeemable warrant, each whole warrant
entitling the holder to purchase one Share at an exercise price of $11.50 per Share, as set forth in the Company’s Registration Statement on Form S-1, filed with the U.S. Securities and Exchange
Commission (the “SEC”), File Number 333-259269 (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”). 

WHEREAS, the Purchaser has agreed to purchase, at a price of $1.50 per warrant, 5,800,000 warrants (or 6,400,000 if the underwriters in the
Public Offering exercise their over-allotment option in full) (the “Private Placement Warrants”), each Private Placement 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 Private Placement Warrants. 

A. Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private
Placement Warrants to the Purchaser. 
 B. Purchase and Sale of the Private Placement Warrants. 

(i) On the date of the consummation of the Public Offering or on such earlier time and date as may be mutually agreed by the
Purchaser and the Company (the “IPO Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, 5,800,000 Private Placement Warrants at a price of $1.50 per warrant for an
aggregate purchase price of $8,700,000 (the “Purchase Price”). The Purchaser shall pay the Purchase Price by wire transfer of immediately available funds to the Company, to the trust account at a financial institution to be chosen
by the Company, maintained by Continental Stock Transfer & Trust Company, acting as trustee (the “Trust Account”), in accordance with the Company’s wiring instructions, at least one (1) business day prior to the
IPO Closing Date. On the IPO Closing Date, upon the payment by the Purchaser of the Purchase Price, by wire transfer of immediately available funds to the Company, the Company, at its option, shall deliver a certificate evidencing the Private
Placement Warrants purchased on such date duly registered in the Purchaser’s name to the Purchaser or effect such delivery in book-entry form. 

(ii) On the date of any closing of the over-allotment option, if any, in connection with the Public Offering or on such earlier
time and date as may be mutually agreed by the Purchaser and the Company (each such date, an “Over-allotment Closing Date”, and each Over-allotment Closing Date (if any) and the IPO Closing Date, a “Closing Date”),
the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to 600,000 Private Placement Warrants (or, to the extent the over-allotment option is not exercised in full, a lesser number of Private
Placement Warrants in proportion to the portion of the over-allotment option that is exercised) at a price of $1.50 per warrant for an aggregate purchase price of up to $900,000 (the “Over-allotment Purchase Price”). The Purchaser
shall pay the Over-allotment Purchase Price to the Trust Account by wire transfer of immediately available funds in accordance with the Company’s wiring instructions, at least one (1) business day prior to such Over-allotment Closing 

 












 Date. On the Over-allotment Closing Date, upon the payment by the Purchaser of the
Over-allotment Purchase Price, by wire transfer of immediately available funds to the Company, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the
Purchaser’s name to the Purchaser or effect such delivery in book-entry form. 
 C. Terms of the Private Placement
Warrants. 
 (i) Each Private Placement Warrant shall have the terms set forth in a Warrant Agreement to be entered into
by the Company and a warrant agent, in connection with the Public Offering (the “Warrant Agreement”), and shall be subject to the terms of a letter agreement to be entered into by the Company, the Purchaser and the other parties
thereto, in connection with the Public Offering. 
 (ii) At the time of, or prior to, the IPO Closing Date, the Company and
the Purchaser shall enter into a registration and stockholder rights agreement (the “Registration Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private
Placement Warrants and the Shares underlying the Private Placement Warrants. 
 Section 2. Representations and
Warranties of the Company. 
 As a material inducement to the Purchaser to enter into this Agreement and purchase the Private Placement
Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive each Closing Date) that: 

A. Incorporation and Corporate Power. The Company is a corporation duly incorporated, 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 Private Placement Warrants have been duly authorized by
the Company as of each Closing Date. This Agreement constitutes the valid and binding obligation of the Company, 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). Upon issuance in accordance with, and payment pursuant to, the terms of the
Warrant Agreement and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of each Closing Date. 

(ii) The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of
the Private Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of and compliance with the respective terms hereof and thereof by the Company, do not and will not as of each Closing Date
(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 amended and restated certificate of incorporation of the Company or the bylaws of the Company (in effect on the date hereof or as may be amended prior to completion of the 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. 

  
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 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 Private Placement 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 Private Placement Warrants purchased by it and the Shares issuable upon exercise of such Private Placement 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. 
 E. Regulation D Qualification. Neither the Company nor, to its actual knowledge, any of its
affiliates, members, officers, directors or beneficial shareholders 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. 

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 Private Placement Warrants to the Purchaser, the
Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive each Closing Date) 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 each Closing Date (a) conflict with or result in a breach by the Purchaser 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 Purchaser’s equity 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 Purchaser’s organizational documents 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 Purchaser is subject, or any agreement, instrument, order, judgment or decree to which the Purchaser is subject, except for any filings required after the date hereof under
federal or state securities laws. 
 C. Investment Representations. 

(i) The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares
issuable upon such exercise (collectively, the “Securities”) for its 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, and
the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

  
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 (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 decide to enter into this Agreement as a result of any general solicitation or general advertising
within the meaning of Rule 502(c) of Regulation D 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. 
 (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. In this regard, the Purchaser understands that the SEC has taken the position that promoters or affiliates of a blank check
company and their transferees, both before and after an initial Business Combination, are deemed to be “underwriters” under the Securities Act when reselling the securities of a blank check company. Based on that position, Rule 144 adopted
pursuant to the Securities Act would not be available for resale transactions of the Securities despite technical compliance with the requirements of such Rule, and the Securities can be resold only through a registered offering or in reliance upon
another exemption from the registration requirements of the Securities Act. 
 (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. 

(ix) The Purchaser understands that the Private Placement Warrants shall bear the legend substantially in the form set forth in
the Warrant Agreement. 
 Section 4. Conditions of the Purchaser’s Obligations. 

The obligations of the Purchaser to purchase and pay for the Private Placement Warrants are subject to the fulfillment, on or before each
Closing Date, of each of the following conditions: 

  
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 A. Representations and Warranties. The representations and warranties
of the Company contained in Section 2 shall be true and correct at and as of such Closing Date 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 such Closing Date. 
 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 and Registration Rights Agreement. The Company shall have entered into the Warrant Agreement and
the Registration Rights Agreement, in each case on terms satisfactory to the Purchaser. 
 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 each Closing Date, 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 such Closing Date 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 such Closing Date. 

C. Corporate Consents. The Company shall have obtained the consent of its Board of Directors authorizing the execution,
delivery and performance of this Agreement and the Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder. 

D. 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. 
 E. Warrant Agreement and Registration
Rights Agreement. The Company shall have entered into the Warrant Agreement and the Registration Rights Agreement, in each case on terms satisfactory to the Company. 

Section 6. Termination. 

This Agreement may be terminated by the Company or the Purchaser at any time after December 31, 2021 upon written notice to the other
party hereto 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 each Closing Date. 

Section 8. Definitions. 

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

  
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 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 (including, without limitation one or more of its members). 

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 shall be deemed to be a contract made under the laws of the State of New York and for
all purposes shall be construed in accordance with the internal laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the laws of another jurisdiction. 

F. Amendments. This 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] 

 

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

			
	COMPANY:
	
	CRIXUS BH3 ACQUISITION COMPANY
		
	By:	 	 /s/ Daniel Lebensohn

	Name:	 	Daniel Lebensohn
	Title:	 	Co-Chief Executive Officer
	
	PURCHASER:
	
	CRIXUS BH3 SPONSOR, LLC
		
	By:	 	 /s/ Gregory Freedman

	Name:	 	Gregory Freedman
	Title:	 	President


 [Signature Page to Warrant Purchase Agreement]