Hi Claire,
I don't have much on the 5th Tennessee Mounted Infantry. I don't think there is much out there on them. You can go to http://www.civilwararchive.com and there will be a listing of Tennessee Union Units. Also, http://www.tngenweb.org/civilwar/rosters/minf/minf5/coh1.htm... . There is a small bit in those listing. I had a g-g-grandfather who fought in Company H of the 5th. Good luck and if I find anything else I will pass it on.