Exhibit 10.5


 


PRIVATE PLACEMENT SHARES PURCHASE AGREEMENT


 


THIS PRIVATE PLACEMENT SHARES PURCHASE AGREEMENT
(as it may from time to time be amended and including all exhibits referenced herein, this “Agreement”), dated
as of May 24, 2021 (the “Effective Date”), is entered into by and between among Fifth Wall Acquisition Corp.
III, a Cayman Islands exempted company (the “Company”), and Fifth Wall Acquisition Sponsor III LLC, a Cayman
Islands limited liability company (the “Purchaser”).


 


WHEREAS, the Company intends to consummate an initial
public offering (the “Public Offering”) of the Company’s Class A ordinary shares, par value $0.0001 (each,
a “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 333-255292 (the “Registration Statement”),
under the Securities Act of 1933, as amended (the “Securities Act”).


 


WHEREAS, the Purchaser has agreed to purchase an
aggregate of 857,000 Shares (and up to 932,000 Shares if the underwriters in the Public Offering exercise their option to purchase additional
Shares in full) (the “Private Placement Shares”).


 


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 Shares.


 


A.               Authorization
of the Private Placement Shares. The Company has duly authorized the issuance and sale of the Private Placement Shares to the Purchaser.


 


B.                Purchase
and Sale of the Private Placement Shares.


 


(i)             On
the date of the consummation of the Public Offering (the “IPO Closing Date”), the Company shall issue and sell
to the Purchaser, and the Purchaser shall purchase from the Company, 857,000 Private Placement Shares at a price of $10.00 per Private
Placement Share for an aggregate purchase price of $8,570,000 (the “Purchase Price”). The Purchaser shall pay
the Purchase Price by wire transfer of immediately available funds to the Company at in accordance with the Company’s wiring instructions,
at least one (1) business day prior to the date of effectiveness of the Registration Statement filed in connection with the Public Offering.
On the IPO Closing Date, subject to the receipt of funds pursuant to the immediately prior sentence, the Company, at its option, shall
deliver a certificate evidencing the Private Placement Shares purchased by the Purchaser 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 option to purchase additional Shares, 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 “Option Closing Date”,
and each Option 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 75,000 Private Placement Shares (or, to the extent
the option to purchase additional Shares is not exercised in full, a lesser number of Private Placement Shares in proportion to portion
of the option that is exercised) at a price of $10.00 per Private Placement Share for an aggregate purchase price of up to $750,000 (the
 “Option Purchase Price”). The Purchaser shall pay the Option Purchase Price in accordance with the Company’s
wire instruction by wire transfer of immediately available funds to the Company. On each Option Closing Date (if any), subject to the
receipt of funds pursuant to the immediately prior sentence, the Company shall, at its option, deliver a certificate evidencing the Private
Placement Shares 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 Shares.


 


(i)             The
Private Placement Shares are substantially identical to the Shares to be offered in the Public Offering except: (a) as provided in that
letter agreement, dated as of the date hereof (the “Letter Agreement”), by and among the Company, the Purchaser
and each of the Company’s officers, directors and director nominees, and (b) the Private Placement Shares are being purchased pursuant
to an exemption from the registration requirements of the Securities Act and will become freely tradable only after the expiration of
the lockup described above in the Letter Agreement and they are registered pursuant to the Registration and Shareholder Rights Agreement
(as defined below) or an exemption from registration is available, and the restrictions described above in clause (a) have expired.


 


(ii)            On the Effective Date, the Company and the Purchaser shall enter into a registration and shareholder rights agreement (the “Registration
and Shareholder Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser
relating to the Private Placement Shares.


 


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
Shares, 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 an exempted company duly incorporated, validly existing and in good standing under the laws of
the Cayman Islands 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.


 






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B.                Authorization; No Breach.


 


(i)             The
execution, delivery and performance of this Agreement and the Private Placement Shares have been duly authorized by the Company as of
the Closing Date. This Agreement constitutes the 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 this Agreement, the Private Placement Shares will constitute
valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Date.


 


(ii)            The execution and delivery by the Company of this Agreement and the Private Placement Shares, the issuance and sale of the Private
Placement Shares 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 share capital 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 memorandum and articles
of association 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, the Private Placement Shares will be
duly and validly issued, fully paid and nonassessable. Upon issuance in accordance with, and payment pursuant to, the terms hereof, the
Purchaser will have good title to the Private Placement Shares purchased by it, 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 Shares to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties
shall survive each Closing Date) that:


 






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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 that would materially impact its
ability to perform its obligations hereunder.


 


C.                Investment
Representations.


 


(i)             The Purchaser is acquiring the Private Placement Shares 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 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 Private Placement Shares 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 Private Placement Shares.


 


(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 Private Placement Shares 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 Private Placement Shares 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 Private Placement Shares.


 






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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 Private Placement Shares or the fairness or suitability of the investment in the Private Placement
Shares by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Private Placement Shares.


 


(vii)         The Purchaser understands that: (a) the Private Placement Shares 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 and Shareholder Rights
Agreement, neither the Company nor any other person is under any obligation to register the Private Placement Shares under the Securities
Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder. While the Purchaser understands
that Rule 144 under the Securities Act is not available for the resale of securities initially issued by shell companies (other than business
combination related shell companies) or issuers that have been at any time previously a shell company, the Purchaser understands that
Rule 144 includes an exception to this prohibition if the following conditions are met: (i) the issuer of the securities that was formerly
a shell company has ceased to be a shell company; (ii) the issuer of the securities is subject to the reporting requirements of Section
13 or 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”); (iii) the issuer of the securities has
filed all Exchange Act reports and material required to be filed, as applicable, during the preceding 12 months (or such shorter period
that the issuer was required to file such reports and materials), other than Form 8-K reports; and (iv) at least one year has elapsed
from the time that the issuer filed current Form 10 type information with the SEC reflecting its status as an entity that is not a shell
company.


 


(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 Private Placement Shares and is able to bear the economic risk of an investment in the Private Placement Shares 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 Private Placement Shares. The Purchaser can afford a complete loss of its investments in the Private Placement Shares.


 


(ix)           The
Purchaser understands that the Private Placement Shares shall bear the following legend and appropriate “stop transfer restrictions”:


 


“THE SECURITIES
REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES
LAWS, AND NEITHER THE SECURITIES NOR ANY INTEREST THEREIN MAY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF EXCEPT
PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT OR SUCH LAWS OR AN EXEMPTION FROM REGISTRATION UNDER SUCH ACT AND
SUCH LAWS WHICH, IN THE OPINION OF COUNSEL, IS AVAILABLE.


 






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THE SECURITIES REPRESENTED BY THIS CERTIFICATE
ARE SUBJECT TO LOCKUP PROVISIONS AND MAY NOT BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF DURING THE TERM OF THE LOCKUP.”


 


Section 4.              Conditions
of the Purchaser’s Obligations. The obligations of the Purchaser to purchase and pay for the Private Placement Shares 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.                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.


 


D.                Registration
and Shareholder Rights Agreement. The Company shall have entered into the Registration and Shareholder Rights Agreement 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 issuance and sale of the Private Placement Shares hereunder.


 






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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.


 


Section 6.               Termination.
This Agreement may be terminated at any time after December 31, 2022 upon the election by either the Company or the Purchaser upon written
notice to the other party if the closing of the IPO 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 on
Form S-1 the Company plans to file under the Securities Act.


 


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 its 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. In the event that any signature is delivered
by via 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.


 






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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 the
parties hereto.


 


[Signature page follows]


 






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IN WITNESS WHEREOF, the undersigned have duly executed
this Agreement as of the date first written above.


 


	 	COMPANY:
	 	 
	 	FIFTH WALL ACQUISITION CORP.
    III,
	 	a Cayman Islands exempted company
	 	 
	 	 
	 	By:	/s/ Brendan Wallace
	 	 	Name: 	Brendan Wallace
	 	 	Title:	Chief Executive Officer
	 	 
	 	PURCHASER:
	 	 
	 	FIFTH WALL ACQUISITION SPONSOR
    III LLC,
	 	a Cayman Islands limited liability
    company
	 	 
	 	 
	 	By:	/s/ Brendan Wallace
	 	 	Name:	Brendan Wallace
	 	 	Title:	Manager




 


[Signature Page to Private Placement Shares Purchase Agreement]