I have been giving this problem probably more thought than I should.....
You can't necessarally associate what is on the discharge with the unit he SERVED with.
It was very often the case that a man served his combat time with one outfit, and then at the conclusion of hostilities or due to requirements elsewhere, he was transfered into another unit to either be demobilized or reassigned. This happened a lot!
The 10th Regiment was part of the 5th Infantry Division.If that is on his discharge then that is the unit he was DISCHARGED WITH.
Until additional information comes up that literally puts him in the 76th for the fighting then you have a problem to solve.
I seem to recall that you mentioned that you ASKED him a direct question in one of your earlier postings---is he still with us?Why not just ask him which outfit he was in.
Keep in mind that the discharge unit COULD be just the one he was out-processed through.He may well have done his time in the 76th and was mustered out with the 10th IR of the 5th ID.And maybe he can identify the other guy in the photo.It might also be that the 8th Division may come into play in your search.
What is this pin you mentioned?Want to send me a jpeg of it?