Exhibit 5.1

	Black Spade Acquisition III Co	Email dbulley@applebyglobal.com
	Suite 2902, 29/F, The Centrium,
	60 Wyndham Street,	Direct Dial +852 2905 5770
	Central,	Tel +852 2523 8123
	Hong Kong	Fax +852 2524 5548
	(the Addressee)
		Your Ref

		Appleby Ref 472626.0001/DRB/DB

		15 October 2026

Black Spade Acquisition III Co (the Company)

Suites 3504B-06

35/F, Two Taikoo Place

979 King’s Road

Quarry Bay

Hong Kong

Tel +852 2523 8123

applebyglobal.com

Managing Partner
David Bulley

Partners

Fiona Chan

Kitty Chan

Vincent Chan

Chris Cheng

Richard Grasby

Judy Lee

Michael Makridakis

John McCarroll SC

Lorinda Peasland

Eliot Simpson

Freya Xu

INTRODUCTION

This opinion as to Cayman Islands law is addressed to you in connection with the Company’s registration statement on Form F-4, including all amendments or supplements thereto, filed with the United States Securities and Exchange Commission (the Commission) under the United States Securities Act of 1933, as amended (the Securities Act) (including its exhibits, the Registration Statement) for the purposes of registering with the Commission under the Securities Act the offering by the Company of up to 162,400,000 Class A ordinary shares of the Company of a par value of US$0.0001 each (each a Class A Ordinary Share and together, the Class A Ordinary Shares), pursuant to certain transactions contemplated by the business combination agreement dated as of 27 August 2026 by and among the Company, Astrum Space Inc and Astrum Networks Pte. Ltd. (as may be amended, supplemented or otherwise modified from time to time, the Business Combination Agreement).

We are furnishing this opinion as Exhibits 5.1 and 23.3 to the Registration Statement and in connection with the Business Combination Agreement.

OUR REVIEW

For the purposes of giving this opinion we have examined and relied upon the documents listed in Schedule 1. We have not examined any other documents.

We have not made any other enquiries concerning the Company and in particular we have not investigated or verified any matter of fact or opinion (whether set out in the Business Combination Agreement or elsewhere) other than as expressly stated in this opinion. Furthermore, we have made no independent investigation of any laws other than the laws of the Cayman Islands.

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LIMITATIONS

Our opinion is limited to, and should be construed in accordance with, the laws of the Cayman Islands at the date of this opinion. We express no opinion on the laws of any other jurisdiction.

This opinion is limited to the matters stated in it and does not extend, and is not to be extended by implication, to any other matters. We express no opinion on the commercial implications of the Business Combination Agreement or whether it gives effect to the commercial intentions of the parties. Except as specifically stated herein, we make no comment with respect to any representations and warranties which may be made by or with respect to the Company in any of the documents or instruments cited in this opinion or otherwise with respect to the commercial terms of the transactions the subject of this opinion.

This opinion is addressed to the Addressee in connection with the matters referred to herein and may be relied upon only by the Addressee, the Addressee’s counsel and subscribers of Class A Ordinary Shares pursuant to the Registration Statement. Except with our prior written consent, this opinion may not be used or relied upon by any other person. This opinion is issued solely for the purposes of the filing of the Registration Statement and the registration of the Class A Ordinary Shares by the Company and is not to be relied upon in respect of any other matter.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the references to our firm under the caption “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving this consent we do not hereby admit that we are experts within the meaning of Section 11 of the Securities Act or that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission promulgated thereunder.

ASSUMPTIONS AND RESERVATIONS

We give the following opinions on the basis of the assumptions set out in Schedule 2 (Assumptions), which we have not verified, and subject to the reservations set out in Schedule 3 (Reservations).

OPINIONS

Incorporation and Status: The Company is an exempted company incorporated with limited liability and existing under the laws of the Cayman Islands and is a separate legal entity. The Company is in good standing with the Registrar of Companies of the Cayman Islands.

Authorised Share Capital: With effect upon the Closing Date (as defined under the Business Combination Agreement), the authorised share capital of the Company will be US$50,000 divided into 400,000,000 Class A ordinary shares of a par value of US$0.0001 each and 100,000,000 preference shares of a par value of US$0.0001 each.

Issue of Class A Ordinary Shares: The issue and allotment of the Class A Ordinary Shares as contemplated by the Registration Statement and the Business Combination Agreement have been duly authorised for issue, and when allotted and issued by the Company against payment in full of the consideration as set out in the Registration Statement and the Business Combination Agreement and in accordance with the terms set out in the Second Amended and Restated Memorandum and Articles (as defined in Schedule 1), such Class A Ordinary Shares will be validly issued, fully paid and non-assessable (meaning that no further sums are payable to the Company on such shares). As a matter of Cayman Islands law, a share is only issued when it has been entered in the register of members (shareholders).

Statements in Registration Statement: The statements set forth in the prospectus forming part of the Registration Statement under the caption “Cayman Islands Tax Considerations”, to the extent that they constitute statements of Cayman Islands law, are accurate in all material respects and that such statements constitute our opinion.

Yours faithfully

Appleby

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Schedule 1

Documents Examined

A copy of the certificate of incorporation of the Company dated 21 August 2025 (the Certificate of Incorporation).

A copy of the amended and restated memorandum and articles of association of the Company adopted on 5 January 2026 (the Existing Memorandum and Articles) and a copy of the draft second amended and restated memorandum and articles of association of the Company to be in effect at the Merger Effective Time (the Second Amended and Restated Memorandum and Articles).

A copy of the certificate of good standing dated 15 October 2026 issued by the Registrar of Companies in respect of the Company (the Certificate of Good Standing).

A copy of the text of the resolutions passed at a meeting of the board of directors of the Company held on 21 August 2026 (the Resolutions) and the full text of the proposed resolutions to be passed by the shareholders of the Company at an extraordinary general meeting of the Company to be held in connection with the proposed business combination, as set out in the Registration Statement (the Shareholder Resolutions).

A copy of the register of directors and officers of the Company dated 15 October 2026 (Register of Directors and Officers).

The Business Combination Agreement.

The Registration Statement.

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Schedule 2

Assumptions

We have assumed:

(i) that the originals of all documents examined in connection with this opinion are authentic, accurate and complete; and (ii) the authenticity, accuracy, completeness and conformity to original documents of all documents submitted to us as copies;

that the signatures, initials and seals on all documents and certificates submitted to us as originals or copies of executed originals are authentic, and the signatures and initials on the Business Combination Agreement or any other document executed by the Company are the signatures and initials of a person or persons authorised by the Company under the Resolutions to execute such document;

that where incomplete documents, drafts or signature pages only have been supplied to us for the purposes of issuing this opinion, the original documents have been duly completed and correspond in all material respects with the last version of the relevant documents examined by us prior to giving our opinion;

that the Registration Statement, the Business Combination Agreement and the Second Amended and Restated Memorandum and Articles do not differ in any material respects from any draft of the same which we have examined and upon which this opinion is based;

that each of the parties to the Business Combination Agreement (other than the Company under Cayman Islands law) is incorporated, organised or registered (as the case may be) and in good standing (where such concept is legally relevant) under the laws which govern its capacity and has the capacity, power and authority, has fulfilled all internal authorisation procedures and completed all applicable filings and formalities, and has obtained all authorisations, approvals, consents, licences and exemptions required under the laws of any relevant jurisdiction to execute, deliver and perform its respective obligations under the Business Combination Agreement and the transactions contemplated thereby and has taken all necessary corporate and other action required and completed all applicable formalities required to authorise the execution of the Business Combination Agreement and the performance of its obligations under them;

the due execution and delivery of the Business Combination Agreement by each of the parties thereto (other than execution by the Company under Cayman Islands law);

that the Business Combination Agreement constitutes legal, valid, binding and enforceable obligations of all parties thereto (save for the Company under Cayman Islands law) in accordance with its governing law;

that the choice of laws as the governing law in the Business Combination Agreement has been made in good faith and is valid and binding under the laws of such jurisdiction (other than the Cayman Islands);

that no party to the Business Combination Agreement by having entered into and performing the transactions contemplated by the Business Combination Agreement will be in breach of any other agreement, deed, trust deed or licence to which it is a party or by which it is bound;

10.

the truth, accuracy and completeness of all representations and warranties or statements of fact or law (other than as to the laws of the Cayman Islands in respect of matters upon which we have expressly opined) made in the Business Combination Agreement;

11.

that the Shareholder Resolutions will be duly passed in the manner prescribed in the Existing Memorandum and Articles and will not be amended, varied or revoked in any respect;

12.

the Company will receive money or money’s worth in consideration for the issue of the Class A Ordinary Shares;

13.

that the Registration Statement has been, or will be, declared effective by the Commission prior to the issuance of the Class A Ordinary Shares; and

14.

that there are no matters of fact or law (excluding matters of Cayman Islands law) which would affect the opinions expressed herein.

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Schedule 3

Reservations

Our opinion is subject to the following:

Good Standing: Our opinion as to good standing is based solely upon receipt of the Certificate of Good Standing issued by the Registrar of Companies. The Company shall be deemed to be in good standing under section 200A of the Companies Act (As Revised) of the Cayman Islands (the Companies Act) on the date of issue of the certificate if all fees and penalties under the Companies Act have been paid and the Registrar of Companies has no knowledge that the Company is in default under the Companies Act.

Title: Legal title to the Class A Ordinary Shares is determined (in the absence of fraud, manifest error or other extraordinary circumstances) by reference to the register of members maintained by the Company (usually but not always at its registered office); however, there are certain limited circumstances where an application may be made to a Cayman Islands court for a determination on whether the register of members reflects the correct legal position. Further, the Cayman Islands court has the power to order that the register of members maintained by a company should be rectified where it considers that the register of members does not reflect the correct legal position. As far as we are aware, such applications are rarely made in the Cayman Islands and for the purposes of the opinion given in paragraph 3, there are no circumstances or matters of fact known to us on the date of this opinion which would properly form the basis for an application for an order for rectification of the register of members of the Company, but if such an application were made in respect of the Company’s Class A Ordinary Shares, then the validity of such shares may be subject to re-examination by a Cayman Islands court.

Non-Assessable: In this opinion, the phrase “non-assessable” means, with respect to the issuance of any shares, that a shareholder shall not, in respect of the relevant shares and in the absence of any contractual arrangements, or any obligations pursuant to the memorandum and articles of association, to the contrary, have any obligation to make further contributions to the Company’s assets (except in exceptional circumstances, such as involving fraud, the establishment of an agency relationship or an illegal or improper purpose or other circumstance in which a court may be prepared to pierce or lift the corporate veil).

Corporate Documents: The Registry of Companies in the Cayman Islands is not public in the sense that copies of the memorandum and articles of association of the Company and information on shareholders is not publicly available and information on directors is limited. We have therefore obtained copies of the corporate documents specified in Schedule 1 and relied exclusively on such copies for the verification of such corporate information.

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