Originally Posted by
The Golden Boy
It helps a bit.
If you figure, through 79 you had the letters with no wrap on the seat tube, and screws in the head badge. So it's a good bet it's 1980 or later.
Then if you figure the 1982 catalog shows the 510/515 with the color options- neither of which is Chestnut. So you know it's earlier than 82.
So 80/81.
Hadn't considered (lack of) headbadge screws! Funny, because I helped someone else narrow down a frame year with that same info. Seems to be more confirmation of 1980 since '81 would have Shimano drop-outs and SCM 555 investment crown. 1980 should have Trek "internal tang" fork crown
found this:
https://www.vintage-trek.com/Trek_gallery710SE.htm

captioned:
"Underside of fork crown showing the reinforcing gusset. In the 1980 brochure, this is called the "Trek integral tang" crown."
That's the fork crown that was used 79/80 and matches mine