To Purchase for Cash Up to 10% or 1,753,886 of its Outstanding Common Shares of Beneficial Interest

THE FUND’S OFFER WILL EXPIRE ON OCTOBER 25, 2023 AT 5:00 P.M., EASTERN TIME,

UNLESS THE OFFER IS EXTENDED.

Eaton Vance Senior Income Trust, a Massachusetts business trust registered under the Investment Company Act of 1940, as amended, as a closed-end management investment company (the “Fund” or “we”), is proposing to purchase for cash up to 1,753,886 (i.e., up to 10%) of its issued and outstanding common shares of beneficial interest at a price per share equal to 98% of its net asset value (“NAV”) per share as of the close of regular trading of the New York Stock Exchange (“NYSE”) on the date the offer expires, or if the offer period is extended, as of the close of regular trading of the NYSE on the newly designated expiration date, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated September 26, 2023, and the related Letter of Transmittal (which together, as they may be amended and supplemented from time to time, constitute the “Offer”). Please furnish copies of the enclosed materials to those of your clients for whom you hold shares registered in your name or in the name of your nominee.

All shares validly tendered before 5:00 p.m., Eastern Time on October 25, 2023 or the latest date to which the Fund extends the Offer (the later of October 25, 2023 and the latest time or date to which the Offer is extended is hereafter called the “Expiration Date”) and not properly withdrawn will be purchased by the Fund at a price per share equal to 98% of its NAV per share as of the close of regular trading of the NYSE on the Expiration Date, subject to the terms and conditions of the Offer, including proration provisions. All shares that the Fund does not accept for purchase because of proration will be returned at the Fund’s expense to the shareholders that tendered such shares promptly after the Expiration Date.

As described in the Offer to Purchase, if more than 10% or 1,753,886 shares are validly tendered and not properly withdrawn before the Expiration Date, then the Fund will purchase validly tendered shares tendered at a price per share equal to 98% of its NAV per share as of the close of regular trading of the NYSE on the Expiration Date on a pro rata basis (disregarding fractional shares). As such, shareholders cannot be assured that all of their tendered shares will be repurchased.

The Offer is not conditioned on any minimum number of shares being tendered. The Offer is, however, subject to other conditions. See Sections 1 and 13 of the Offer to Purchase.

For your information and for forwarding to your clients for whom you hold shares registered in your name or in the name of your nominee, we are enclosing the following documents:

2. Form of Letter to Clients, which you may send to your clients for whom you hold shares registered in your name or in the name of your nominee, with an accompanying Instruction Form provided for obtaining such clients’ instructions with regard to the Offer;

3. Form of Letter of Transmittal, for your use and for the information of your clients, together with accompanying instructions, Internal Revenue Service Form W-9 and the instructions included therewith;

4. Return envelope addressed to Equiniti Trust Company, LLC, the depositary for the Offer (the “Depositary”).

WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. THE FUND’S OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., EASTERN TIME, ON OCTOBER 25, 2023, UNLESS THE OFFER IS EXTENDED.

No fees or commissions will be payable to brokers, dealers, commercial banks, trust companies or any person for soliciting tenders of shares under the Offer other than fees paid to EQ Fund Solutions, LLC, the information agent for the Offer (the “Information Agent”), as described in the Offer to Purchase. We will, however, upon request, reimburse or cause to be reimbursed brokers, dealers, commercial banks and trust companies for reasonable and necessary costs and expenses incurred by them in forwarding the enclosed materials to their customers who are beneficial owners of shares held by them as a nominee or in a fiduciary capacity. We will pay or cause to be paid any stock transfer taxes applicable to our purchase of shares pursuant to the Offer, except as otherwise provided in the Offer to Purchase and Letter of Transmittal (see Instruction 6 of the Letter of Transmittal). No broker, dealer, bank, trust company or fiduciary shall be deemed to be an agent of the Fund, the Information Agent or the Depositary or any affiliate of the foregoing for purposes of the Offer.

For shares to be validly tendered pursuant to the Offer, the Depositary must timely receive confirmation of receipt of such shares under the procedure for book-entry transfer, together with a properly completed and duly executed Letter of Transmittal, including any required signature guarantees or an “agent’s message” (as defined in the Offer to Purchase and the Letter of Transmittal) and any other documents required pursuant to the Offer, all in accordance with the instructions set forth in the Offer to Purchase and Letter of Transmittal.

None of the Fund, its Board of Trustees, Eaton Vance Management, the Fund’s investment adviser, or its Information Agent makes any recommendation to any shareholder as to whether to tender or refrain from tendering any shares. Shareholders should carefully evaluate all information in the Offer, should consult their own investment and tax advisors, and should make their own decisions about whether to tender shares, and, if so, how many shares to tender. The Offer is not being made to (nor will tenders be accepted from or on behalf of) shareholders in any jurisdiction in which the making of the Offer or the acceptance thereof would not be in compliance with the laws of such jurisdiction.

Please address any inquiries you may have with respect to the Information Agent at its address set forth on the back cover page of the Offer to Purchase and telephone number set forth below.

You may obtain additional copies of the enclosed material from the Information Agent by calling it at: (888) 542-7446.

Capitalized terms used but not defined herein have the meanings assigned to them in the Offer to Purchase and the Letter of Transmittal.

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY OTHER PERSON AN AGENT OF THE FUND, THE INFORMATION AGENT OR THE DEPOSITARY OR ANY AFFILIATE OF THE FOREGOING, OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN.