If by "later piece" you mean post war, yes, that is correct. I checked Burnside's first delivery of Spencers and it was April 15, 1865. So by the time your serial number was made the Civil War was long over. But as I said before they do have strong Indian War/Western association. The definitive book is "Spencer Repeating Firearms", by Roy Marcot. Other books with less specific coverage are Flayderman's Guide to Antique American Firearms; Civil War Guns by William B. Edwards; Carbines of the Civil War by John D. McAulay; and U.S. Civil War Carbines by Whisker, Yantz, and Hartzler.
And be careful not to clean TOO MUCH. Trust me, it says Model **1865**. Burnside did not even enter into the contract until mid-late 1864.