On my 19-5 the serial # is behind the wooden grips on the butt (have to remove grips to see it) and on the crane behind the cylinder just below the model#
Is it a 2.5" or a 4"/6"? The serial number on a 2.5" will only be on the bottom of the butt but it will also be stamped in the yoke cut on a 4" or 6" 19-5.