Exhibit 10.5

VECTOR ACQUISITION CORPORATION III

One Market Street, Steuart Tower, 23rd Floor

San Francisco, California 94105

May [●], 2021

Vector Acquisition Partners III, L.P.

One Market Street, Steuart Tower, 23rd Floor

San Francisco, California 94105

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 Vector Acquisition Corporation 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”), Vector Acquisition Partners III, L.P. (the “Sponsor”) shall take steps directly or indirectly to make available to the Company certain office space, secretarial and administrative services as may be required by the Company from time to time, situated at One Market Street, Steuart Tower, 23rd Floor, San Francisco, California 94105 (or any successor location). In exchange therefor, the Company shall pay Sponsor a sum of $10,000 per month on the Effective Date and continuing monthly thereafter until the Termination Date. Sponsor 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.

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.

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]

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[Signature Page to Administrative Services Agreement]