The first production 5 inch 629 was the Classic in 1990, and it was a 629-3 with an L-frame style full length underlug.
I have a 629 8-3/8, either a no dash or a -1 (no barrel pin but recessed cylinder) and if it were a 5 incher, the lettering would be centered. Cutting it to 5 inches was my plan until Hamilton Bowen quit working on S&W's. My guess is the seller measured it incorrectly, just to the front of the frame, and rounded that off to the next whole number.
If the seller can send you photos, that would help, especially of the muzzle, and front sight from the top.