Most of the Barkers in the original 5th KY Infantry (Oct. 1861 to Oct. 1862) included my g-grandfather Henry M. Barker, his brothers George W., John C. and perhaps William L.
Their father William Barker Sr. was also in the 5th (Co. A) and was killed at Ivy Mt. Nov. 8, 1861.
If you are referring to this John C. (Calhoun) Barker (1834- after 1912) and who was married to Catherine Lemaster, as far as I have been able to determine, he mustered out with his siblings and never reenlisted. The only one to do so was George W. who joined Co. D of the reogranized 5th. He served until the end of the war and moved to Missouri. He lived to be 92.
John C. Barker lived out the rest of his live at Low Gap, KY
GB