Exhibit 10.5



FORM OF PRIVATE PLACEMENT

WARRANTS PURCHASE AGREEMENT


 


THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT,
dated as of [ ], 2021 (as it may from time to time be amended, this “Agreement”), is entered into by and between Acropolis
Infrastructure Acquisition Corp., a Delaware corporation (the “Company”), and Acropolis Infrastructure Acquisition
Sponsor, L.P., a Cayman Islands exempted limited partnership (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-fifth 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, filed with the Securities and Exchange Commission (the “SEC”), File Number 333-254409 (the “Registration
Statement”), under the Securities Act of 1933, as amended (the “Securities Act”). The Purchaser has agreed
to purchase an aggregate of 6,966,667 warrants (or up to 7,766,667 warrants if the underwriters’ over-allotment option in connection
with the Public Offering is exercised in full) (the “Private Placement Warrants”), each whole 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 closing of the Public Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company
(the “Initial Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from
the Company, 6,966,667 Private Placement Warrants at a price of $1.50 per warrant for an aggregate purchase price of $10,450,000 (the
 “Purchase Price”). The Purchaser shall pay the Purchase Price by wire transfer of immediately available funds to the
Company in accordance with the Company’s wiring instructions. On the Initial Closing Date, upon the payment by the Purchaser of
the Purchase Price, the Company shall either, 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 the closing of the underwriters’ over-allotment option 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 Initial Closing Date being sometimes referred to herein as a “Closing Date”),
the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to 800,000 Private Placement
Warrants, in the same proportion as the amount of the underwriters’ over-allotment option that is exercised, at a price of $1.50
per warrant for an aggregate purchase price of up to $1,200,000 (if the underwriters’ over-allotment option in connection with the
Public Offering is exercised in full) (the “Over-allotment Purchase Price”). The Purchaser shall pay the Over-allotment
Purchase Price by wire transfer of immediately available funds to the Company in accordance with the Company’s wiring instructions.
On the Over-allotment Closing Date, upon the payment by the Purchaser of the Over-allotment Purchase Price, the Company shall either,
at its option, deliver a certificate evidencing the Private Placement Warrants 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”).


 


(ii)            At
or prior to the time of the closing of the Public Offering, 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 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.           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 Private Placement Warrants have been duly authorized by the Company as of
the Closing Date. 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 Private Placement
Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Date.


 






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(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 the 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 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 Private
Placement Warrants will be duly and validly issued and the Shares issuable upon exercise of the Private Placement Warrants will be duly
and validly issued, fully paid and non-assessable. On the date of issuance of the Private Placement Warrants, the Shares issuable upon
exercise of the Placement Warrants shall have been reserved for issuance. 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 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 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.


 






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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 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 Private Placement Warrants and, upon exercise of the Private Placement 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.


 






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(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.


 


(viii)            The
Purchaser has such knowledge and experience in financial and business matters, understands 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 investment in the Securities.


 


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:


 


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.            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.


 






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


 


Section 6.               Termination.
This Agreement may be terminated at any time after December 31, 2021 upon the election by either the Company or the Purchaser upon
written notice to the other party 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.


 


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 without the prior
written consent of the other party hereto, other than assignments by the Purchaser to affiliates thereof (including, without limitation
one or more of its partners or 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.


 






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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. In the event that any signature is delivered
by facsimile transmission or by e-mail delivery of a “pdf” format data file, 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 facsimile
or “.pdf” signature page were an original thereof.


 


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 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:
	 	 
	 	ACROPOLIS INFRASTRUCTURE ACQUISITION CORP.
	 	 
	 	By:	 
	 	 	Name: James Crossen
	 	 	Title: Chief Financial Officer, Chief Accounting Officer and Secretary
	 	 
	 	ACROPOLIS INFRASTRUCTURE ACQUISITION SPONSOR, L.P.
	 	 
	 	By: AP Caps II Holdings GP, LLC, its general partner
	 	 
	 	By: Apollo Principal Holdings III, L.P., its managing member
	 	 
	 	By: Apollo Principal Holdings III GP, Ltd., its general partner
	 	 
	 	By:	 
	 	 	Name: James Elworth
	 	 	Title: Vice President
	 	 




[Signature
Page to Private Placement Warrants Purchase Agreement]