Sylvester Keely is recorded as Silvester Keely at:

Index to the Register of the Sixty-second Regiment of Infantry US Civil War. Source: Annual Report of the Adjutant-General of the State of New York, For the Year 1900

Sylvester was one of the original enlistees in the Anderson Zouaves - 62d NY Volunteer Infantry. His name appears as Sylvester Keely in the document linked below:

Muster Rolls Of The New York Infantry Regiments During The Civil War

Sylvester Keely enlisted as a Private, aged 31, in Company I., on May 28, 1861 at "Union Course" by company commander Captain Lafata. He enlisted for 3 years.

"Union Course" was a nationally famous racetrack situated in the area now bounded by 78th Street, 85th Street, Jamaica Avenue and Atlantic Avenue. The Union Course was the first skinned (dirt) racing surface, a curious novelty at the time. The course was originally without grandstands. - Wikipedia

From an enquiry to our Research Site from Sylvester Keely's relative, Kelly O'Shea