A couple of points and questions - if its a Model 10 its post 1957, Smith didn't start the model numbering system until '57. Open the cylinder, look in the frame cutout where the yoke matches up and if its a Model 10 it will be so stamped there,
i.e. MOD 10-5, or MOD 10-7, etc. The -number indicates the revision change. The other numbers there are assembly numbers and are not the serial number.
Check your serial number again, on the butt of the revolver, and be sure to let us know if there is a letter prefix, i.e. C 12345678 or S 9876543.
Can you post pictures? They would really help. Post back and one of us will be able to give you an appox. date out of the SCSW, but a factory letter would be more precise.