S&W .38 5 shot, exposed hammer, 2.5 in. barrel, s/n 13378.
I assume you're refering to a modern swing out cylinder gun and not an old break top model.
It would be a Chiefs Special. SN 13378 (taken from the underside of the grip butt) would be 1952. SN's ran from 7369 to 21342 that year.