By that format, according to Browning;
Yours should be a 1971 vintage, serial number 5xxx1.In 1969 Browning started using two digits for the date of manufacture which was followed by a four digit code that identified the type of Auto-5:
This was then followed by the serial number beginning with 1000.
Example: 69G1000 = A 1969 Auto-5 Lightweight 12 ga.. shotgun with a serial number of 1000.
Nothing shows what a "Z" code should be, M being a "standard" and G being a "light". They reference those to 12-gauge, I wonder if Z would be a code for one of the 20-gauge versions, or some manner of "limited edition" model.
Also, there have been unique limited edition models that did not follow our regular serial number configurations and they are not included in this listing.