For $3.00 you can order the New York State military records for Daniel Sullivan, who was in Co. A, 5th Reg. NY Heavy Artillery. Go to:
http://iarchives.nysed.gov/CivilWarWeb/search.jspHe's listed, and you can easily print out and order his records. I don't know how extensive they are.
Daniel received a Civil War pension, as did his widow later (as per the Civil War pension index card). You can order his pension records through NARA, using Form NATF 85.
http://archives.gov/veterans/military-service-records/pre-ww... This will cost $75.00 for the complete packet, which will include up to 100 pages. It should include important information and answers for you.
The pension records for my great-great-grandfather who died at Port Hudson,La. were extensive. Information about his death, widow and children was tremendous, and I'd never have found out most of it anywhere else.
Good luck in your searches.