Exhibit 10.5


 


PROPTECH INVESTMENT CORPORATION II


3415 N. Pines Way, Suite 204

Wilson, WY 83014


 


December 3, 2020


 


HC PROPTECH PARTNERS II LLC


3415 N. Pines Way, Suite 204


Wilson, WY 83014


 


Re: Administrative
Support Agreement


 


Ladies and Gentlemen:


 


This letter agreement
by and between PropTech Investment Corporation II (the “Company”) and HC Proptech Partners II LLC (“HC”),
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 Capital Market (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”) and continuing until the earlier
of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described
in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):


 


(i) HC shall make available,
or cause to be made available, to the Company, at 3415 N. Pines Way, Suite 204, Wilson, WY 83014 (or any successor location
of HC), certain office space, utilities and secretarial and administrative support as may be reasonably required by the Company.
In exchange therefor, the Company shall pay Trimaran the sum of $15,000 per month on the Listing Date and continuing monthly thereafter
until the Termination Date; and


 


(ii) HC hereby irrevocably
waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this letter
agreement (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 stockholders of the Company and into which substantially all of the proceeds
of the Company’s initial public offering will be deposited (the “Trust Account”) as a result of, or arising out
of, this letter agreement, and hereby irrevocably waives any Claim it may have in the future, 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 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.


 


No party hereto may
assign either this letter 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.


 


This letter agreement
constitutes the entire relationship of the parties hereto, and 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, without giving effect to its choice of law principles.


 


[Signature Page Follows]


 




     


     


    

 


	
        
	Very truly yours,
	 	 
	 	PROPTECH INVESTMENT CORPORATION II
	 	 	 
	 	By:	/s/ Thomas D. Hennessy
	 	 	Name: Thomas D. Hennessy
	 	 	Title: Co-Chief Executive Officer and President


 


AGREED TO AND ACCEPTED BY:


HC PROPTECH PARTNERS II LLC


 


	By:	/s/ M. Joseph Beck	 
	 	Name: M. Joseph Beck	 
	 	Title:   Managing Member	 


 


[Signature Page to Administrative Support
Agreement]