UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D/A

Under the Securities Exchange Act of 1934

(Amendment No. 5)*

BlackRock New York Municipal Income Trust

(Name of Issuer)

Common Shares, $0.001 par value

(Title of Class of Securities)

09248L106

(CUSIP Number)

Saba Capital Management, L.P.

405 Lexington Avenue

58th Floor

New York, NY 10174

Attention: Michael D'Angelo

(212) 542-4635

(Name, Address and Telephone Number of Person

Authorized to Receive Notices and Communications)

May 17, 2024

(Date of Event Which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of Rule 13d-1(e), Rule 13d-1(f) or Rule 13d-1(g), check the following box. [ ]

(Page 1 of 6 Pages)

______________________________

* The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

CUSIP No. 09248L106

SCHEDULE 13D/A

Page 2 of 6 Pages

1	NAME OF REPORTING PERSON Saba Capital Management, L.P.
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP		(a) ☐ (b) ☐
3	SEC USE ONLY
4	SOURCE OF FUNDS OO (see Item 3)
5	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDING IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)		☐
6	CITIZENSHIP OR PLACE OF ORGANIZATION Delaware
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:	7	SOLE VOTING POWER -0-
	8	SHARED VOTING POWER 2,195,495
	9	SOLE DISPOSITIVE POWER -0-
	10	SHARED DISPOSITIVE POWER 2,195,495
11	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH PERSON 2,195,495
12	CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES		☐
13	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 9.10%
14	TYPE OF REPORTING PERSON PN; IA

The percentages used herein are calculated based upon 24,117,105 Common Shares outstanding as of 1/31/24, as disclosed in the Issuer’s N-CSRS filed 4/3/24.

CUSIP No. 09248L106

SCHEDULE 13D/A

Page 3 of 6 Pages

1	NAME OF REPORTING PERSON Boaz R. Weinstein
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP		(a) ☐ (b) ☐
3	SEC USE ONLY
4	SOURCE OF FUNDS OO (see Item 3)
5	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDING IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)		☐
6	CITIZENSHIP OR PLACE OF ORGANIZATION United States
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:	7	SOLE VOTING POWER -0-
	8	SHARED VOTING POWER 2,195,495
	9	SOLE DISPOSITIVE POWER -0-
	10	SHARED DISPOSITIVE POWER 2,195,495
11	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH PERSON 2,195,495
12	CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES		☐
13	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 9.10%
14	TYPE OF REPORTING PERSON IN

The percentages used herein are calculated based upon 24,117,105 Common Shares outstanding as of 1/31/24, as disclosed in the Issuer’s N-CSRS filed 4/3/24.

CUSIP No. 09248L106

SCHEDULE 13D/A

Page 4 of 6 Pages

1	NAME OF REPORTING PERSON Saba Capital Management GP, LLC
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP		(a) ☐ (b) ☐
3	SEC USE ONLY
4	SOURCE OF FUNDS OO (see Item 3)
5	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDING IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)		☐
6	CITIZENSHIP OR PLACE OF ORGANIZATION Delaware
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:	7	SOLE VOTING POWER -0-
	8	SHARED VOTING POWER 2,195,495
	9	SOLE DISPOSITIVE POWER -0-
	10	SHARED DISPOSITIVE POWER 2,195,495
11	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH PERSON 2,195,495
12	CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES		☐
13	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 9.10%
14	TYPE OF REPORTING PERSON OO

The percentages used herein are calculated based upon 24,117,105 Common Shares outstanding as of 1/31/24, as disclosed in the Issuer’s N-CSRS filed 4/3/24.

CUSIP No. 09248L106

SCHEDULE 13D/A

Page 5 of 6 Pages

Item 1.	SECURITY AND ISSUER

	This Amendment No. 5 amends and supplements the statement on Schedule 13D filed with the SEC on 9/29/23, as amended by Amendment No. 1 filed 12/4/23, Amendment No. 2 filed 1/22/24, Amendment No. 3 filed 2/20/24, and Amendment No. 4 filed 4/8/24; with respect to the common shares of BlackRock New York Municipal Income Trust. This Amendment No. 5 amends Items 4 and 7 as set forth below.

Item 4.

PURPOSE OF TRANSACTION

Item 4 is hereby amended and supplemented as follows:

The Reporting Persons issued the investor presentation (the “Investor Presentation”) attached hereto as Exhibit 3 to shareholders (such exhibit to be deemed incorporated by reference in its entirety into this Item 4) providing their views on the Issuer and its Board, including value-unlocking steps it believes the Issuer should take.

Item 7.	MATERIAL TO BE FILED AS EXHIBITS

Exhibit 3:	Investor Presentation, incorporated herein by reference to the DFAN14A filed with the Securities and Exchange Commission on May 20, 2024.

CUSIP No. 09248L106

SCHEDULE 13D/A

Page 6 of 6 Pages

SIGNATURES

After reasonable inquiry and to the best of his or its knowledge and belief, each of the undersigned certifies that the information set forth in this statement is true, complete and correct.

Date: May 21, 2024

	SABA CAPITAL MANAGEMENT, L.P. By: /s/ Michael D'Angelo
	Name: Michael D'Angelo Title: Chief Compliance Officer


	SABA CAPITAL MANAGEMENT GP, LLC By: /s/ Michael D'Angelo Name: Michael D'Angelo Title: Authorized Signatory


	BOAZ R. WEINSTEIN By: /s/ Michael D'Angelo
	Name: Michael D'Angelo
	Title: Attorney-in-fact*
* Pursuant to a power of attorney dated as of November 16, 2015, which is incorporated herein by reference to Exhibit 2 to the Schedule 13G filed by the Reporting Persons on December 28, 2015, accession number: 0001062993-15-006823

BLACKROCK NEW YORK MUNICIPAL INCOME TRUST SC 13D/A