If anyone is searching for William Underwood from the state of Delaware during the Civil War, check out the Delaware Public Archives site (http://archives.delaware.gov/CivilWar/index.shtml). The Delaware Archives has digitized their Civil War records and slides 0702 through 0705 indicate William Underwood served as a Private in the 5th Reg't Delaware Infantry and in Capt. Hounsfield's Co. 5 Reg't Del. Inf.
Mustered in Oct 25, 1862 and Mustered out Aug. 10, 1863.
Hope this might be of help to someone.