Yes, it is a .38 Military & Police model with a 5" barrel from about 1951. But ship dates in that serial range are a bit mixed up. Here are some examples:
C151763 shipped in April, 1951
C151961 shipped in February, 1952
C152420 shipped in February, 1951
C155209 shipped in May, 1950
The plastic faux stag grips are, of course, an aftermarket addition.