Far be it for me to question the answer given by 2 of our more knowlegable members but I do not see a J in the serial given by guner thus I would think that it is the pre 69 series thus middle 1960s. Welcome to the forum guner.
From the dates that I know of on model 36s in the 500000 range I would say that yours should be 1967 but the only positive way to get the actual date is ask Smith & Wesson Historian Roy Jinks. A $50 letter would probably be a little expensive unles it is something you have to know. Standard Catalog of Smith & Wesson will give you an idea but Smith & Wesson does not ship or even manufacture guns in serial number order and I have seen dates that were years off from the expected ship date.