Support Services Agreement, dated January 12, 2022, between the Company and the Sponsor

Exhibit 10.5

Consilium Acquisition Corp I, Ltd.
2400 E. Commercial Boulevard, Suite 900

Ft. Lauderdale, FL 33308

January 12, 2022

Consilium Acquisition Sponsor I, LLC

2400 E. Commercial Boulevard, Suite 900

Ft. Lauderdale, FL 33308

Re: Support Services Agreement

Ladies and Gentlemen:

This Support Services Agreement (this “Agreement”) by and between Consilium Acquisition Corp I, Ltd., a Cayman Islands exempted company (the “Company”) and Consilium Acquisition Sponsor I, LLC, a Cayman Islands limited liability company (the “Provider”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on The Nasdaq Stock Market LLC (the “Listing Date”) and continuing until the earlier of the consummation by the Company of an initial business combination and the Company’s liquidation (in each case as described in the Registration Statement on Form S-1 (File No. 333-261570) filed with the Securities and Exchange Commission) (such earlier date hereinafter referred to as the “Termination Date”), the Provider shall make available to the Company, at 2400 E. Commercial Boulevard, Suite 900, Ft. Lauderdale, FL 33308 (or any successor location or other existing office locations of the Provider or any of its affiliates), certain office space, administrative and support services as may be reasonably requested by the Company. In exchange therefor, the Company shall pay the Provider the sum of $10,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date.

The Provider hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public shareholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, this Agreement, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

This 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 Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto.

No party hereto may assign either this Agreement or any of its rights, interests or obligations hereunder without the prior written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

Any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York.

This 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.

[Signature page follows]

[Signature Page to Support Services Agreement]