Seven round cylinder? You might want to check again that should be a six round cylinder. Smith did not start producing 7 shot centerfire revolvers until the 90's (?).
Judging by the serial number you have a K-frame revolver. Open the cylinder and look at the frame under the barrel. There should be a model number stamped there. Maybe a model 10? If there is no model number, how many side plate screws? Look under the barrel and above/ in front of the trigger guard. Smith's are normally grouped by the number of screws they have. Modern guns have 3 screws all in the side plate. Prior to that they had 4 screws, the three in the side plate and one in the front of the trigger guard. even earlier they had a 4th side plate screw on top near the hammer nose.
Hence the designations of 3, 4 or 5 screw models.
5 screw models are pre-WWII. 4 screws are up to about '61/'62.