The serial No is 77921 which puts it made in 1958 I believe but I am far from a historian for S&W. The deal I read stated that "a lighter 5 inch barrel was introduced in 1958 for field use." That is in Wikipedia.

I edited this to include the whole serial No. Figure maybe the historians at S & W might read this and have some record of her. She has a 5 1/2 inch barrel.