Exhibit 10.5

POWER & DIGITAL INFRASTRUCTURE ACQUISITION CORP.
321 North Clark Street, Suite 2440
Chicago, IL 60654

February 9, 2021

XPDI Sponsor LLC
321 North Clark Street, Suite 2440
Chicago, IL 60654

Ladies and Gentlemen:

This letter will confirm our agreement that, commencing on the effective date (the “Effective Date”) of the registration statement (the “Registration Statement”) for the initial public offering (the “IPO”) of the securities of Power & Digital Infrastructure Acquisition Corp. (the “Company”) and continuing until the earlier of (i) the completion by the Company of an initial business combination or (ii) the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”), XPDI Sponsor LLC (the “Sponsor”) shall take steps directly or indirectly to make available to the Company certain office space, secretarial and administrative services (including without limitation certain financial modeling and related services) as may be required by the Company from time to time, situated at 321 North Clark Street, Suite 2440, Chicago, IL 60654 (or any successor location). In exchange therefore, the Company shall pay affiliates of the Sponsor a sum of $20,000 per month on the Effective Date and continuing monthly thereafter until the Termination Date. The Sponsor hereby agrees that it does not have any right, title, interest or claim of any kind 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 (the “Claim”) and hereby 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.

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[Signature Page to Administrative Services Agreement]

[Signature Page to Administrative Services Agreement]