James Vidrine:
That is an oldie. If the following matches, then its a S&W .38 Military & Police 1st Model, also known as the Model of 1899 Army-Navy Revolver, manufactured in the serial range 1-20,975 between 1899 & 1902.
The barrel should be marked .38 S&W Special CTG & US Service CTG. on the left side.
There should not be a lug attached to the barrel in front of the ejector rod.
Grips will be hard rubber with a molded S&W logo or plain walnut.
Your Dad's gun falls in the period 1900-1901 (serial range 5000 - 14000), 1900 seems likely.
A few caveats: This was the first .38 special firearm, smokeless pistol powder was very new. It predates heat treatment of cylinders by 20 years and the positive internal hammer block safety by 44 years. If it is to be shot, stick to lead only standard pressure/velocity rounds. No PlusP, +P+, jacketed or jacketed hollow point ammo. Leave the chamber under the hammer empty until ready to fire, that way there is no chance of the gun firing if dropped.