UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 5)¹

Eaton Vance Senior Income Trust

(Name of Issuer)

Common Shares, $0.01 par value

(Title of Class of Securities)

27826S103

(CUSIP Number)

Saba Capital Management, L.P.

405 Lexington Avenue

58th Floor

New York, New York 10174

Attention: Michael D’Angelo

(212) 542-4635

Olshan Frome Wolosky LLP

1325 Avenue of the Americas

New York, New York 10019

Attention: Adam W. Finerman, Esq.

(212) 451-2300

(Name, Address and Telephone Number of Person

Authorized to Receive Notices and Communications)

October 30, 2020

(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 §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box ☒.

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See § 240.13d-7 for other parties to whom copies are to be sent.

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¹       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).

The percentages used herein are calculated based upon 37,866,607 common shares outstanding as of 05/30/2020, as disclosed in the Issuer’s N-CSRS filed 8/26/2020.

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¹ A portion of the shares are held by Saba Closed-End Funds ETF, which will vote its shares pursuant to its Statement of Additional Information.

The percentages used herein are calculated based upon 37,866,607 common shares outstanding as of 05/30/2020, as disclosed in the Issuer’s N-CSRS filed 8/26/2020.

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² A portion of the shares are held by Saba Closed-End Funds ETF, which will vote its shares pursuant to its Statement of Additional Information.

The percentages used herein are calculated based upon 37,866,607 common shares outstanding as of 05/30/2020, as disclosed in the Issuer’s N-CSRS filed 8/26/2020.

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³ A portion of the shares are held by Saba Closed-End Funds ETF, which will vote its shares pursuant to its Statement of Additional Information.

This Amendment No. 5 amends and supplements the statement on Schedule 13D filed with the SEC on June 8, 2020, as amended on July 21, 2020, August 3, 2020, August 6, 2020 and August 8, 2020, with respect to the Common Shares of Eaton Vance Senior Income Trust. This Amendment No. 5 amends Items 3,4,5,6 and 7 as set forth below.

Item 3 is hereby amended and restated as follows:

Funds for the purchase of the Common Shares were derived from the subscription proceeds from investors and the capital appreciation thereon and margin account borrowings made in the ordinary course of business.  In such instances, the positions held in the margin accounts are pledged as collateral security for the repayment of debit balances in the account, which may exist from time to time.  Since other securities are held in the margin accounts, it is not possible to determine the amounts, if any, of margin used to purchase the Common Shares reported herein. A total of approximately $45,060,659 was paid to acquire the Common Shares reported herein.

Item 4 is hereby amended and supplemented as follows:

On October 30, 2020, Saba Capital filed a preliminary proxy statement with the Securities and Exchange Commission seeking to oppose the Issuer’s proposal to approve a new management agreement at the Issuer’s Special Meeting of Shareholders scheduled to be held on January 7, 2021 (the “Special Meeting”).

As one of the largest shareholders of the Issuer, Saba Capital does not believe it is in the best interest of shareholders to approve a new management agreement with Eaton Vance Management because the Issuer currently trades at a significant discount to NAV. Saba Capital believes that, in a situation such as this, where the Issuer has and is trading at an excessive discount to NAV, managers should not be automatically approved, and Saba Capital believes it could be beneficial to consider alternatives.

Item 5 is hereby amended and restated to read as follows:

(a) See rows (11) and (13) of the cover pages to this Schedule 13D/A for the aggregate number of Common Shares and percentages of the Common Shares beneficially owned by each of the Reporting Persons.  The percentages used herein are calculated based upon 37,866,607 common shares outstanding as of 5/30/2020, as disclosed in the Issuer's N-CSRS filed 8/26/2020.

(b) See rows (7) through (10) of the cover pages to this Schedule 13D/A for the number of Common Shares as to which each Reporting Person has the sole or shared power to vote or direct the vote and sole or shared power to dispose or to direct the disposition.

(c) The Reporting Persons have not entered into any transactions in the Common Shares during the past sixty days.

(d) The funds and accounts advised by Saba Capital have the right to receive the dividends from and proceeds of sales from the Common Shares.

(e) Not applicable.

Item 6 is hereby amended and supplemented as follows:

On November 2, 2020, the Reporting Persons entered into a Joint Filing and Solicitation Agreement in which, among other things, (a) the Reporting Persons agreed to the joint filing on behalf of each of them of statements on Schedule 13D with respect to the securities of the Issuer, (b) the Reporting Persons agreed to solicit proxies to oppose the Issuer’s proposal to approve a new management agreement at the Special Meeting (the “Solicitation”), and (c) Saba Capital agreed to bear all expenses incurred in connection with the Solicitation. The Joint Filing and Solicitation Agreement is attached hereto as Exhibit 99.1 and is incorporated herein by reference.

Item 7 is hereby amended to add the following exhibit:

99.1       Joint Filing and Solicitation Agreement as required by Rule 13d-1(k)(1) under the Act.

SIGNATURES

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

Date: November 3, 2020

JOINT FILING AND SOLICITATION AGREEMENT

WHEREAS, certain of the funds and accounts managed by Saba Capital Management, L.P. are shareholders, direct or beneficial, of Eaton Vance Senior Income Trust, a Massachusetts business trust (the “Fund”);

WHEREAS, Saba Capital Management, L.P., Saba Capital Master Fund, Ltd., Saba II AIV, L.P., Saba Capital Master Fund III, L.P., Saba Capital Carry Neutral Tail Hedge Master Fund Ltd., Saba Capital W Fund, Ltd., Saba Capital R Fund, Ltd., Saba Capital CEF Opportunities 1, Ltd., Saba Capital CEF Opportunities 3, Ltd., Saba Capital Special Opportunities Fund, Ltd. and Boaz R. Weinstein (collectively, “Saba”), wish to form a group for the purpose of opposing the Fund’s proposal to approve a new management agreement at the Fund’s Special Meeting of Shareholders scheduled to be held on January 7, 2021 (including any adjournments, postponements, reschedulings or continuations thereof, the “Special Meeting”) and for soliciting shareholder support for any proposal submitted by any member of the Group (as defined below) and for the purpose of taking all other action necessary to achieve the foregoing.

NOW, IT IS AGREED, this 2^nd day of November 2020 by the parties hereto:

1.       In accordance with Rule 13d-1(k)(1)(iii) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), each of the undersigned (collectively, the “Group”) agrees to the joint filing on behalf of each of them of statements on Schedule 13D, and any amendments thereto, with respect to the securities of the Fund. Each member of the Group shall be responsible for the accuracy and completeness of his/its own disclosure therein, and is not responsible for the accuracy and completeness of the information concerning the other members, unless such member knows or has reason to know that such information is inaccurate.

2.       So long as this agreement is in effect, each of the undersigned shall provide written notice to Olshan Frome Wolosky LLP (“Olshan”) of (i) any of their purchases or sales of securities of the Fund or (ii) any securities of the Fund over which they acquire or dispose of beneficial ownership. Notice shall be given no later than 24 hours after each such transaction. For purposes of this agreement, the term “beneficial ownership” shall have the meaning of such term set forth in Rule 13d-3 under the Exchange Act.

3.       Each of the undersigned agrees to form the Group for the purpose of (i) soliciting proxies to oppose the Fund’s proposal to approve a new management agreement and any proposal submitted by any member of the Group to shareholders for their approval, each at the Special Meeting, (ii) taking such other actions as the parties deem advisable and (iii) taking all other action necessary or advisable to achieve the foregoing.

4.       Saba shall have the right to pre-approve all expenses incurred in connection with the Group’s activities and agrees to pay directly all such pre-approved expenses.

5.       Each of the undersigned agrees that any SEC filing, press release or shareholder communication proposed to be made or issued by the Group or any member of the Group in connection with the Group’s activities set forth in Section 3 shall be as directed by Saba.

6.       The relationship of the parties hereto shall be limited to carrying on the business of the Group in accordance with the terms of this agreement. Such relationship shall be construed and deemed to be for the sole and limited purpose of carrying on such business as described herein. Nothing herein shall be construed to authorize any party to act as an agent for any other party, or to create a joint venture or partnership, or to constitute an indemnification. Nothing herein shall restrict any party’s right to purchase or sell securities of the Fund, as he/it deems appropriate, in his/its sole discretion, provided that all such purchases and sales are made in compliance with all applicable securities laws and the provisions of this agreement.

7.       This agreement may be executed in counterparts, each of which shall be deemed an original and all of which, taken together, shall constitute but one and the same instrument, which may be sufficiently evidenced by one counterpart.

8.       This agreement is governed by and will be construed in accordance with the laws of the State of New York. In the event of any dispute arising out of the provisions of this agreement or their investment in the Fund, the parties hereto consent and submit to the exclusive jurisdiction of the United States District Court for the Southern District of New York located in the Borough of Manhattan or the courts of the State of New York located in the County of New York.

9.       Any party hereto may terminate his/its obligations under this agreement on 24 hours’ written notice to all other parties, with a copy by e-mail to Adam W. Finerman of Olshan at afinerman@olshanlaw.com.

10.       Each party acknowledges that Olshan shall act as counsel for both the Group and Saba relating to their investment in the Fund.

11.       Each of the undersigned parties hereby agrees that this agreement may be filed as an exhibit to a Schedule 13D pursuant to Rule 13d-1(k)(1)(iii) under the Exchange Act.

IN WITNESS WHEREOF, the parties hereto have caused this agreement to be executed as of the day and year first above written.

* 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