If you want to know the build date post the first few numbers of the serial number and someone may help you . 645 is a 2nd Generation pistol 1979 -88 steel frame hooked trigger guard and side protectors ( ears) for adjustable sights . Other variations have fixed sights and rounded trigger guards. I have seen other pistols with wood panels with medallions on top but don't know if they are factory. nice pistol!
Welcome to the Forum,
My Model 645 is identical to your's but they came from S&W with black plastic grip panels. I purchased mine new in very early 1988. I would assume your's dates to 1987 like mine. Mine is serial# TBF9436. I replaced the black plastic grips (they are in the box) with Model 745 walnut grips.
very nice looking pistol you got there I appreciate the info. mine shoots awesome but I'm still fighting the ambidextrous saftey I have tried thread lock but to no success i shoot no more than a magazine and i have to tighten it iv seen alot of people online having the same issue