The first four digits of the number you posted are the model: 3365. That comes back to a 1956 7.5hp. You can also reverse the last two digits of the model to get the year: 3365 = 1956.
Additionally, the 1957 Abos Guide I have lists 1001 as the starting sequential # for 1956 on that model. So the balance of your number 5686 would be the number produced minus 1001. (i.e. you have the 4685th 7.5 hp motor produced that year) To the best of my recollection, I’m not aware of anything published by S/A regarding production numbers – so the Abos info is all I have unless someone else has something from the factory. (Presumably Abos got their info from S/A!)