Hello Randy,
Being a flag expert, based on what corps the 5th/35th Tennessee served in at Shiloh, they should have carried a Buckner/Hardee pattern battleflag since thwey were part of Pat Clebrune's Brigade of Hardee's Corps. This was the battle flag of that corps. They were blue with a white disc in the center and the unit designation painted on the disc.
For more on this type of flag please see our Flags of the Confederacy website at www.confederateflags.org
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Greg Biggs