Unless a person has the list of guns made and ser.# for each year made called a blue book you cannot tell the exact year. However these were made 1937 to 1976 and then discontinued. they are valued at in good condition at $650 plain barrel, $700 with raised rib, and $800 ventilated rib. They were Reintroduced in 1987 as the new model and are valued at $475-$500 in real good condition. The 'Sweet Sixteen' was introduced into the Browning catalogs in 1936, but your gun was made about five years earlier. It is a standard-weight 16ga Browning Auto-5. It should be either a plain barrel gun or a solid-rib gun. They are not as desireable as the later guns because they have the 2 9/16" chamber which is not compatible with modern ammunition. Still, they can reach $500-$600 in excellent condition. Original, actual 'Sweet Sixteen' guns in excellent condition are routinely bringing $1500 at auction, and even Miroku-made Japanese Sweet Sixteens can be counted on for $900-$1000. However, yours is a pre-war standard Auto-5 and not a Sweet Sixteen.
Your browning sweet sixteen was made by FN of belguim for browning in 1957,with the serial numbe that you provided.
your browning sweet-sixteen with the serial number you provided was made by browning in belgium by FN in 1956.
That is not a Sweet Sixteen serial number.
Your browning sweet sixteen was made by browning in 1953.
your browning sweet sixteen was made in 1959.
your browning sweet sixteen was made in 1955.
Your browning sweet sixteen was made by browning in 1953.
With the serial number that you provided,your browning sweet sixteen shotgun was made by FN of belguim for browning in 1928.
Your Browning sweet sixteen was made in the year 1955 with the serial number that you have provided.
Your browning sweet sixteen shotgun was made by FN of belguim for browning in 1961.
your browning sweet sixteen with a 2s prefix was made in 1962.
Serial number s76529.The serial number S76529 indicates that your Browning sweet sixteen shotgun was made in the year 1957.