By the serial number.
Your serial number indicates that your Smith and Wesson 38 special was made in the Year 1960.
Yes, they have made hundreds of thousands.
1962
Made in 1979.
Made @ 1964.
Without a sn, there is no way to answer.
@ 1975
Made by the Performance Center.
@ 53
Never made by S&W
Shipped from the factory @ 1970
With the serial number that you have supplied,your Smith and Wesson model 10-5 was made in the years 1972-1973.