Yesterday my gift to myself arrived. I won a 5" M&P 38 special on Gunbroker. The serial number is C2221XX which should be 1951 according to SCSW It has honest wear and was probably carried by a right hander since the right stock is beat up more than the left. I put the targets on because the magnas just don't fit my hand. I cleaned it up last night and took it to the range today. Very smooth double action. The target is 48 rounds at 7 yards, 158 gn LSWC. I'm very happy with it.
C2221xx was made in 1952 (probably late in the year), but I show several with SNs not too far distant from yours which shipped in 1953 and even 1954. One sees many old cop guns with one grip showing much more wear and damage than the other, resulting from years of bumping into things while holstered. Your non-relieved targets are a bit out of the ordinary. A shame they appear to have been refinished.
My 5" is C1847XX which I was told was probably shipped in 1952 - which is my birth year. Anyway, it is my "go to" Smith - there is just something about a 5" that "feels rigth' in my hand - and it is an excellent shooter too! You are really going to enjoy yours - congrats on your find!