I have a S-W five-shot .38SW revolver. It is a break-action. I can only find what I assume is a serial number on bottom of the grips. The number is 407865.
S&W used the same serial numbers on different models, but the only top-break model in .38 S&W that reached the 400000 level was the .38 Double Action. This gun had an exposed hammer and you must have one of those. The serial number suggests your gun was shipped in 1900 or 1901, so it may be quite a bit older than you suspected.
Post pics if you can. That would help us confirm my guess.
Thanks, DC. According to Smith-Wesson, it is a .38 Double Action Fourth Model, sold in September, 1900. The serial number is 407865.
I can't send a photo yet, due to being on restrictions as a new member.