I will give a second opinion that 1965 may be right there in the wheelhouse. The fantastic book that we used that tipoc mentioned above is very good with SN look up for a lot of S&W guns but it's extremely vague for pistols in this SN range for whatever reason, most likely because S&W did a lot of unpredictable things when it came to SN's and rotation and storage of stock. It has been suggested that there was a lot of "First In, Last Out" and detailed records searching has sometimes shown literally YEARS between ship dates of guns that are extremely close in range.
The easy answer that a lot of the hardcore guys who are knee-deep in to the lore and mystery of S&W is always simply that S&W was in the business of selling guns and they had no care whatsoever for collectibles and for doing things in any manner of any predictable order, they simply had the goal of making guns and selling and shipping, using EVERY PART possible, all the time.
Some folks have had luck calling S&W and asking for a ship date by giving the SN over the phone. That call is free but I believe the older guns are not in the system these folks on the phone will use if you call now.
The reason that I believe the 1965 is likely is that I have a Model 39 no-dash that is a 31xxx serial number and I've been digging through many discussions overs the few years I have owned it, and the date that I keep coming up with is 1964. Also note that I have never seen a Model 39 with a 5-digit SN in the range of 5xxxx, I believe that the 5xxxx range was was used for the Model 52 guns, starting with 50000 in 1961. I am unsure if any Model 41/46's used the 5xxxx range, but I have never seen a 39 that has.
Hey... now that I think about it, I don't think I've seen any 4xxxx SN's in Model 39's either. But I can tell you this... there are a couple active guys on that other forum who will know the ranges that 39's have appeared, far better than me.
All of that is a long way of explaining that my 31xxx and your 61530 may sound a lot of numbers away from each other, but I don't think they are that far at all.
The little Model 61 Escort, .22LR pistols, I don't know what number range they used. I only bring them up because the 5-digit number with no alpha and the later A-prefix and 6-digit SN's were all used exclusively for semi-auto pistols. And between 1961 and 1970, that means models 39, 41, 46, 52 and 61 except for the oddities that were not made in volume. While it seems like S&W made fifteen thousand different semi-auto pistol models, they made only those five models back in those days. The Model 59 came around in the early 1970's, and the 2nd Gen pistols arrived in 1982 or 1983.