Document:

Exhibit 10.4

 

Cactus Acquisition Corp. 1 Limited

4B Cedar Brook Drive

Cranbury, NJ 08512

 

May 21, 2021

Cactus Healthcare Management LP

4B Cedar Brook Drive

Cranbury, NJ 08512

 

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 Cactus Acquisition Corp.’s (the “Company”) securities and continuing
until the earlier of (i) the consummation 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”),
Cactus Healthcare Management LP shall, or shall cause its affiliates to, make available to the Company certain office space, utilities,
secretarial support and other administrative support and services as may be required by the Company from time to time, situated at 4B
Cedar Brook Drive, Cranbury, NJ 08512 (or any successor location). In exchange therefore, the Company shall pay Cactus Healthcare Management
LP the sum of $10,000 per month on the Effective Date and continuing monthly thereafter until the Termination Date. Cactus Healthcare
Management LP 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”) to 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.

 

[Signature Page Follows]

 

     

     

    

 

		Very truly yours,
	 	 
	 	Cactus Acquisition Corp. 1 Limited
	 	 
	 	By: 	/s/ Ofer Gonen
	 	 	Name: 	Ofer Gonen
	 	 	Title:	 Chief Executive Officer

 

AGREED TO AND ACCEPTED BY:

 

Cactus Healthcare
Management LP

 

	By: 	Cactus Healthcare Management LLC,	 
	 	its sole General Partner

 

	By: 	/s/ Stephen T. Wills	 
	 	Name: 	 Stephen T. Wills	 
	 	Title: 	Secretary	 

 

[Signature
Page to Administrative Services Agreement]Exhibit 10.5

 

PRIVATE WARRANTS PURCHASE AGREEMENT BETWEEN
THE REGISTRANT AND

CACTUS HEALTHCARE MANAGEMENT LP.

  

THIS PRIVATE WARRANTS PURCHASE AGREEMENT, dated as
of November 2, 2021 (as it may from time to time be amended, this “Agreement”), is entered into by and between Cactus Acquisition
Corp. 1 Limited, a Cayman Islands exempted company (the “Company”), and Cactus Healthcare Management LP, a Delaware limited
partnership (the “Purchaser”).

 

RECITALS

 

WHEREAS, the Company intends to consummate an initial
public offering (the “Public Offering”) of the Company’s units (the “Units”), each Unit consisting of one
Class A ordinary share of the Company, par value $0.0001 per share (each, an “Ordinary Share”), and one-half (1/2) of
one warrant (a “Warrant”) (each whole Warrant entitles the holder to purchase one Ordinary Share at a price of $11.50 per
share); and

 

WHEREAS, the Purchaser has agreed to purchase an
aggregate of 4,866,667 Warrants (the “Sponsor Warrants”).

 

NOW THEREFORE, in consideration of the mutual promises
contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the
parties to this Agreement hereby, intending legally to be bound, agree as follows:

 

AGREEMENT

 

Section 1. Authorization, Purchase and Sale;
Terms of the Sponsor Warrants.

 

(a) Authorization of the Sponsor Warrants. The Company
has duly authorized the issuance and sale of the Sponsor Warrants to the Purchaser.

 

(b) Purchase and Sale of the Sponsor Warrants.

 

(i) On the date of the consummation of the Public
Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company (the “Closing Date”),
the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, 4,866,667 Sponsor Warrants at a
price of $1.50 per Warrant for an aggregate purchase price of $7,300,000 (the “Purchase Price”), which shall be paid by wire
transfer of immediately available funds to the Company at least one day prior to the Initial Closing Date in accordance with the Company’s
wiring instructions. On the Initial Closing Date, following the payment by the Purchaser of the Purchase Price by wire transfer of immediately
available funds to the Company, the Company, at its option, shall deliver a certificate evidencing the Sponsor Warrants purchased on such
date, duly registered in the Purchaser’s name to the Purchaser, or effect such delivery in book-entry form.

 

(c) Terms of the Sponsor Warrants.

 

(i) Each Sponsor Warrant shall have the terms set
forth in a Warrant Agreement to be entered into by the Company and a warrant agent, in connection with the Public Offering (a “Warrant
Agreement”), and shall be subject to the terms of a letter agreement, dated as of the date hereof, to be entered into by the Company,
the Purchaser and the other parties thereto, in connection with the Public Offering.

 

(ii) At the time of, or prior to, the Initial Closing
Date, the Company and the Purchaser shall enter into a registration rights agreement (the “Registration Rights Agreement”)
pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Sponsor Warrants and the Ordinary
Shares underlying the Sponsor Warrants.

 

     

     

    

 

(iii) The Purchaser hereby agrees not to transfer,
assign or sell any of the Sponsor Warrants and the Ordinary Shares underlying the Sponsor Warrants, until 30 days after the Company’s
completion of its initial business combination transaction. The foregoing transfer restrictions shall not apply to transfers by the Purchaser
or by the recipient of any below-described transfer (such recipient, a “Permitted Transferee”):

 

(a) to the Company’s
officers or directors, any affiliates or family members of the Company’s officers or directors, any members of the Purchaser, or
any affiliates of the Purchaser;

 

(b) in the case of an
individual, by gift to a member of the individual’s immediate family or to a trust, the beneficiary of which is a member of the
individual’s immediate family or an affiliate of such person, or to a charitable organization;

 

(c) in the case of
an individual, by virtue of laws of descent and distribution upon death of the individual;

 

(d) in the case of an individual,
pursuant to a qualified domestic relations order;

 

(e) by private sales or transfers
made in connection with the consummation of a business combination at prices no greater than the price at which the securities were originally
purchased;

 

(f) in the event of the
liquidation of the Company prior to the Company’s completion of its initial business combination;

 

(g) by virtue of the laws of
the Cayman Islands or the Purchaser’s exempted limited partnership agreement, as amended, upon liquidation of the Purchaser; or

 

(h) in the event of the Company’s
completion of a liquidation, merger, amalgamation, share exchange, reorganization or other similar transaction which results in all of
its shareholders having the right to exchange their Ordinary Shares for cash, securities or other property subsequent to the Company’s
completion of its initial business combination;

 

provided, however, that except
with the Company’s prior consent, in the case of clauses (a) through (e), or (g), above, the Permitted Transferee
must enter into a written agreement agreeing to be bound by these transfer restrictions and by the same agreements entered into by the
Purchaser with respect to the Sponsor Warrants (including provisions relating to voting, the trust account and liquidation distributions,
as described in the prospectus forming a part of the Company’s registration statement on Form S-1).

 

Section 2. Representations and Warranties of the
Company.

 

As a material inducement to the Purchaser to enter
into this Agreement and purchase the Sponsor Warrants, the Company hereby represents and warrants to the Purchaser (which representations
and warranties shall survive each Closing Date) that:

 

(a) Organization and Corporate Power. The Company
is an exempted company duly incorporated, validly existing and in good standing under the laws of the Cayman Islands and is qualified
to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect
on the financial condition, operating results or assets of the Company. The Company possesses all requisite corporate power and authority
necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement.

 

(b) Authorization; No Breach.

 

(i) The execution, delivery and performance of this
Agreement and the Sponsor Warrants have been duly authorized by the Company as of the Closing Date. This Agreement constitutes the valid
and binding obligation of the Company, enforceable in accordance with its terms. Upon issuance in accordance with, and payment pursuant
to, the terms of this Agreement and the Warrant Agreement, the Sponsor Warrants will constitute valid and binding obligations of the Company,
enforceable in accordance with their terms as of the Closing Date.

 

(ii) The execution and delivery by the Company of
this Agreement and the Sponsor Warrants, the issuance and sale of the Sponsor Warrants, the issuance of the Ordinary Shares upon exercise
of the Sponsor Warrants and the fulfillment, of and compliance with, the respective terms hereof and thereof by the Company, do not and
will not as of each Closing Date (A) conflict with or result in a breach of the terms, conditions or provisions of, (B) constitute a default
under, (C) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s share capital or assets
under, (D) result in a violation of, or (E) require any authorization, consent, approval, exemption or other action by or notice or declaration
to, or filing with, any court or administrative or governmental body or agency pursuant to, the amended and restated memorandum and articles
of association of the Company (in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering),
or any material law, statute, rule or regulation to which the Company is subject, or any agreement, order, judgment or decree to which
the Company is subject, except for any filings required after the date hereof under federal or state securities laws.

 

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(c) Title to Securities.

 

Upon issuance in accordance with, and payment pursuant
to, and registration in the register of members of the Company, the terms hereof and the Warrant Agreement, the Ordinary Shares issuable
upon exercise of the Sponsor Warrants will be duly and validly issued, fully paid and non-assessable. Upon issuance in accordance with,
and payment pursuant to, the terms hereof and the Warrant Agreement, the Purchaser will have good title to the Sponsor Warrants, and the
Ordinary Shares issuable upon exercise of such Sponsor Warrants, free and clear of all liens, claims and encumbrances of any kind, other
than (i) transfer restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal
and state securities laws, and (iii) liens, claims or encumbrances imposed due to the actions of the Purchaser.

 

(d) Governmental Consents.

 

No permit, consent, approval or authorization of,
or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by
the Company of this Agreement or the consummation by the Company of any other transactions contemplated hereby.

 

Section 3. Representations and Warranties of the
Purchaser.

 

As a material inducement to the Company to enter
into this Agreement and issue and sell the Sponsor Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company
(which representations and warranties shall survive the Closing Date) that:

 

(a) Organization and Requisite Authority. The Purchaser
possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

 

(b) Authorization; No Breach.

 

(i) This Agreement constitutes a valid and binding
obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization,
moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles
(whether considered in a proceeding in equity or law).

 

(ii) The execution and delivery by the Purchaser
of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser does not and shall not as of each Closing
Date conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of any agreement, instrument, order,
judgment or decree to which the Purchaser is subject.

 

(c) Investment Representations.

 

(i) The Purchaser is acquiring the Sponsor Warrants,
and, upon exercise of the Sponsor Warrants, the Ordinary Shares issuable upon such exercise (collectively, the “Securities”),
for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with, any
public sale or distribution thereof.

 

(ii) The Purchaser is an “accredited investor”
as such term is defined in Rule 501(a)(3) of Regulation D under the Securities Act of 1933, as amended (the “Securities Act”).

 

(iii) The Purchaser understands that the Securities
are being offered and will be sold to it in reliance on specific exemptions from the registration requirements of the United States federal
and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the
representations and warranties of the Purchaser set forth herein in order to determine the availability of such exemptions and the eligibility
of the Purchaser to acquire such Securities.

 

(iv) The Purchaser decided to enter into this
Agreement not as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act.

 

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(v) The Purchaser has been furnished with all materials
relating to the business, finances and operations of the Company and materials relating to the offer and sale of the Securities which
have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors
of the Company. The Purchaser understands that its investment in the Securities involves a high degree of risk and it has sought such
accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition
of the Securities.

 

(vi) The Purchaser understands that no United States
federal or state agency or any other government or governmental agency has passed on or made any recommendation or endorsement of the
Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or
endorsed the merits of the offering of the Securities.

 

(vii) The Purchaser understands that: (a) the Securities
have not been and are not being registered under the Securities Act or any state securities laws, and may not be offered for sale, sold,
assigned or transferred unless (1) in a registered transaction or (2) sold in reliance on an exemption therefrom; and (b) except
as specifically set forth in the Registration Rights Agreement, neither the Company nor any other person is under any obligation to register
the resale of the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption
thereunder. In this regard, the Purchaser understands that the Securities and Exchange Commission (the “SEC”) has taken the
position that promoters or affiliates of a blank check company and their transferees, both before and after a “business combination”,
are deemed to be “underwriters” under the Securities Act when reselling the securities of a blank check company. Based on
that position, Rule 144 adopted pursuant to the Securities Act would not be available for resale transactions of the Securities despite
technical compliance with the requirements of such Rule, and the Securities can be resold only through a registered offering or in reliance
upon another exemption from the registration requirements of the Securities Act.

 

(viii) The Purchaser has such knowledge and experience
in financial and business matters, knows of the high degree of risk associated with investments in the securities of companies in the
development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to
bear the economic risk of an investment in the Securities in the amount contemplated hereunder for an indefinite period of time. The Purchaser
has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs
for liquidity which would be jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investments
in the Securities.

 

Section 4. Conditions of the Purchaser’s Obligations.

 

The obligations of the Purchaser to purchase and
pay for the Sponsor Warrants are subject to the fulfillment, on or before the Closing Date, of each of the following conditions:

 

(a) Representations and Warranties. The representations
and warranties of the Company contained in ‎Section 2 shall be true and correct at and as of the Closing Date as though then made.

 

(b) Performance. The Company shall have performed
and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied
with by it on or before the Closing Date.

 

(c) No Injunction. No litigation, statute, rule,
regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court
or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated
hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

 

(d) Warrant Agreement. The Company shall have entered
into a Warrant Agreement with a warrant agent on terms satisfactory to the Purchaser.

 

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Section 5. Conditions of the Company’s
Obligations. The obligations of the Company to the Purchaser under this Agreement are subject to the fulfillment, on or before each Closing
Date, of each of the following conditions:

 

(a) Representations and Warranties. The representations
and warranties of the Purchaser contained in ‎Section 3 shall be true and correct at and as of such Closing Date as though then made.

 

(b) Performance. The Purchaser shall have performed
and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied
with by the Purchaser on or before the Closing Date.

 

(c) No Injunction. No litigation, statute, rule,
regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court
or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated
hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

 

(d) Warrant Agreement. The Company shall have entered
into a Warrant Agreement with a warrant agent on terms satisfactory to the Company.

 

Section 6. Termination. This Agreement may be terminated
at any time after [●], 2021 upon the election by either the Company or the Purchaser upon written notice to the other party if the
closing of the Public Offering does not occur prior to such date.

 

Section 7. Survival of Representations and Warranties.
All of the representations and warranties contained herein shall survive each Closing Date.

 

Section 8. Definitions. Terms used but not otherwise
defined in this Agreement shall have the meaning assigned to such terms in the registration statement on Form S-1 the Company has filed
with the SEC, under the Securities Act.

 

Section 9. Miscellaneous.

 

(a) Successors and Assigns. Except as otherwise expressly
provided herein, all covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto shall bind and
inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or
anything to the contrary herein, the parties may not assign this Agreement, other than assignments by the Purchaser to affiliates thereof.

 

(b) Severability. Whenever possible, each provision
of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this
Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such
prohibition or invalidity, without invalidating the remainder of this Agreement.

 

(c) Counterparts. This Agreement may be executed
simultaneously in two or more counterparts, none of which need contain the signatures of more than one party, but all such counterparts
taken together shall constitute one and the same agreement.

  

(d) Descriptive Headings; Interpretation. The
descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement. The
use of the word “including” in this Agreement shall be by way of example rather than by limitation.

 

(e) Governing Law. This Agreement shall be deemed
to be a contract made under the laws of the State of New York and for all purposes shall be construed in accordance with the internal
laws of the State of New York.

 

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

 

[Signature Page Follows]

 

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IN WITNESS WHEREOF, the parties hereto have executed
this Agreement to be effective as of the date first set forth above.

 

	COMPANY:	 
	Cactus Acquisition Corp. 1 Limited	 
	 	 
	By:	/s/ Ofer Gonen	 
	 	Name:  	Ofer Gonen	 
	 	Title: 	Chief Executive Officer	 
	 	 	 
	PURCHASER:	 
	 	 	 
	Cactus Healthcare Management LP	 
	Acting by Cactus Management LLC,

its sole General Partner
	 	 
	By:	/s/ Stephen T. Wills	 
	 	Name: 	Stephen T. Wills	 
	 	Title: 	Secretary

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