Hello.
My own great grandfather was James Thomas Harper (1840-1928) and he fought with the 5th Tenn. and was wounded at Shiloh.
Now that I have found your posting, I cannot help but wonder if he marched with them. I know he supposedly fought around Atlanta because we believe that was where he was wounded again. In one Tennessee site, Harper is listed as being killed at Atlanta, but that did not happen because he fathered at least twelve children after that.
If I could find my local cemetery book, I could tell you which company of the 5th Harper served with for sure.
I think you already probably understand that finding a marked grave is going to be hard, at least that has been my experience.
More than likely if he was buried by the Confederates, the Union moved his grave after the war and at that time most nearly all the deceased CSA soldiers became an unknown.
But my advice is no matter what, keep searching.
Good luck-
Linda