Exhibit 10.5

PERIDOT ACQUISITION CORP. III

2229 San Felipe Street, Suite 1450
Houston, Texas 77019

[], 2021

[]
2229 San Felipe Street, Suite 1450
Houston, Texas 77019

Ladies and Gentlemen:

This letter agreement, by and between Peridot Acquisition Corp. III and [ ] (“Affiliate”), an affiliate of our sponsor, Peridot Acquisition Sponsor III, LLC (“Sponsor”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities are first listed on the New York Stock Exchange (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”) for the initial public offering (the “IPO”) of the securities of Peridot Acquisition Corp. III (the “Company”) and continuing until the earlier of (i) the consummation by the Company of an initial business combination and (ii) the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

(i)

Affiliate shall take steps directly or indirectly to make available (or cause other persons to make available) to the Company certain office space, secretarial and administrative support as may be required by the Company from time to time, situated at 2229 San Felipe Street, Suite 1450, Houston, Texas 77019 (or any successor location of Affiliate). As reimbursement therefor, the Company shall pay Affiliate (and Affiliate will receive on behalf of itself or, to the extent it causes another person to make support available to the Company, as nominee on behalf of such other person), a sum of $40,000 per month beginning on the Listing Date and continuing monthly thereafter until the Termination Date upon which, at the Affiliate’s option, Company shall pay Affiliate an amount equal to $960,000 less any amounts previously paid.

(ii)

Affiliate hereby agrees that it does not have any right, title, interest or claim of any kind (a “Claim”) in or to any monies that may be set aside in a trust account (the “Trust Account”) that may be established upon the consummation of the IPO and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, any negotiations, contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever. Although the sums payable hereunder are fixed, the parties intend that such sums constitute solely a reimbursement for the costs described herein without any mark-up or other profits and agree that such fixed sums constitute a reasonable estimate of such costs.

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.

The parties may not assign this letter agreement and any of their rights, interests, or obligations hereunder without the consent of the other party; provided, however, that Affiliate may assign this letter agreement, in whole or in part, to Sponsor or any other person that directly, or indirectly through one or more intermediaries, controls, or is controlled by, or is under common control with, Sponsor without the prior written approval of the Company.

This letter agreement 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 laws principles that will apply the laws of another jurisdiction.

This letter agreement may be executed in one or more counterparts, each of which shall for all purposes be deemed to be an original but all of which together shall constitute one and the same agreement. Only one such counterpart signed by the party against whom enforceability is sought needs to be produced to evidence the existence of this letter agreement.

[Signature Page Follows]

Very truly yours,

PERIDOT ACQUISITION CORP. III

By:

Name: Stephen Wedemeyer
Title: Chief Financial Officer

[Signature Page to Administrative Services Agreement]

AGREED TO AND ACCEPTED BY:

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By:

Name:
Title:

[Signature Page to Administrative Services Agreement]

Peridot Acquisition Corp. III S-1