Assuming it’s a 12 gauge, there should be none of the barrel extension protruding from the receiver. If there is, the forearm has been battered and is due to crack.
Speaking of forearm cracks, check the bottom, many have cracks there.
A lot of parts were updated in 1958, if you’re only going to have one, a ‘58 or later will be easier to find parts for. These guns are identified by a single digit (1958-67) or two digits (1967-76) in front of the serial number’s letter prefix.
When I check an Auto-5, I cover the primers of dummy cartridges with tape. I load the gun, and cycle it by pulling the barrel all the way back and releasing. Ejected cartridges should have only the smallest dent in the tape. Then I repeat, this time pulling the trigger and checking for a strong hole in the tape.