The 1860 census reports Riley Byrd, age twenty, in Scott County, Tenn. I don't see a CSR under this name or anything similar. Do you have a pension application for him?
This command organized at Memphis, Tenn., with companies from Alabama, Arkansas, Kentucky and Florida. Assuming that officers and men were Tennesseans, the War Department mistakenly designated it the 40th Tennessee Regiment. Their mistake was corrected a few months later, and it became Walker's 5th Confederate Regiment.
Aside from the coincidence mentioned (the name "Minter", an officer from Dale County, Ala.), can you explain how or why someone from a remote part of Tennessee would be in this regiment?