You can check with S&W Customer service for a more precise date, but the Model 10, change #5 was made from about 1962-1967. Value will depend on condition and exact variant, but somewhere in the $200-$250 range would be average for a good condition revolver.
Your serial number indicates that your Smith and Wesson 38 special was made in the Year 1960.
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$9.92
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With the serial number that you have supplied,your Smith and Wesson model 37 was made in the year 1981.