look on the opposite side of the gun, there should be an engraving stating where it was manufactured, if it is Belguim, it was made before 1976, if it was Japan, it could have been made in the late 80s.
Your browning sweet sixteen shotgun was made by FN of belguim for browning in 1961.
CHeck the receiver.
Look on the receiver.
browning sweet sixteen serial number 5s43804 what year was it manufactured
Check the receiver, barrel
The Browning Sweet sixteen, will have the words "Sweet Sixteen" stamped or engraved on the receiver after the 1948-1950 time period. Prior to Sweet Sixteen being engraved on the legend which is the left side of the receiver, Sweets from 1937-40 and 46-49 are not stamped. If you have one of these guns, the gun will have a faded gold trigger - not blued. This is the most obvious sign. To be sure remove the forend. If the Barrel ring that slides over the magazine tube has three holes in it, then it is a sweet, providing the barrel serial number matches the receiver. So, check the trigger and barrel. Two other differences can be detected, but it's more info than needed to answer your question.
1965
Your best bet is to call Browning.
With the serial number you provided,Your browning sweet-sixteen auto-5 shotgun was made by FN of belguim for browning in 1956.
Your browning auto-5 sweet sixteen was made by FN of belguim for browning in 1951.
1965
This gun was made in 1948