FWIW, Model 29-5 serial BKY78xx was shipped in May 1992. Be advised that S&W didn't ship in serial number sequence. The only way to know when your 29-5 left the factory is to request a letter or submit a ship date request on the S&WCA member side of this board.
I have a 629-3 5" Classic with BKV prefix and 29-6 6.5" Classic with BRD prefix. I believe the BKV prefix is 1993 and BRD is 1994. Have not lettered either.
.44 Special ammo is just fine in your 29-5 and it's easier on the hands for casual shooting and target practice. The cylinder chambers are slightly longer than .44 Special brass cases so you may have to brush the chambers to get the crud out.
BTW, I'm curious, is your 29-5 hammer and trigger case-colored or flash chromed?
Here's my beloved 29-6, "Big Blue".
1994_Model 29-6_Classic_.44 Mag_Krein05Walkabout.JPG