The actual serial number is the one on the butt, as noted above. That number should also be seen on the underside of the barrel and the rear face of the cylinder as well as a couple of more less obvious places. I hate to disagree with a fellow forum member about a serial number, but I think that gun has to be from about 1919-20 -- there are six digits to the SN, not five.
Notice the mushroom-shaped ejector rod. Serial number aside, that by itself means it was produced before about 1928. Also there is no small S&W logo on the left side of the gun, and I doubt there is a large one on the sideplate. That also points to production in the immediate post WWI era. There should be some patent stamps on the barrel, with the last one dating to 1914.
The rubber stocks are recent, of course, but probably conceal a round butt grip frame. If so, that's a little interesting, because most of the M&P production in the 'teens, '20s and '30s consisted of square butt frames.
S&W took steps to harden their steel in about 1922, so this gun predates that step. Don't shoot +P ammo or self-announced hot loads. I usually shoot 148 gr match wadcutter loads in my older .38s.
Nice gun, easily worth $275.