STOP! Proceed with caution...
Double check the left side of the barrel. See if it says "65" in small print. Prior to sometime in the 1930s, the 16ga A5s were made with 2 9/16" chambers. If yours is one of those guns, and you are shooting modern 2 3/4" shells, then I would expect that it wouldn't eject properly.
I would also expect that it is dangerous to continue doing so.
I just ran down to the safe and am holding my 1930 16ga A5. To check if yours might have the short chambers:
1) Open the bolt and verify that the gun is unloaded.
2) Peform Step 1 until you are SURE.
3) Press down on the barrel and forearm (pulling them towards the receiver), while you unscrew the magazine cap.
4) On the left side of the barrel, look for a small proof mark. It will probably be an oval with two numbers in it. One of those will be a 16 (for the gauge), the other will be the chamber length, in millimeters.
If the second number is 70, then you've got a 2 3/4" chamber, and modern ammo should be OK. If it says 65, then it was made with a 2 9/16" chamber. In that case, 2 3/4" ammo is not safe. Fortunately, you can order 2 1/2" shells from a number of places on the net. They're not cheap, but they work well and are (most importantly) safe!
In any event, you may want to have a knowledgable smith check things out anyway. Some of the short chambered guns were modified (chambers reamed, ejection ports lengthened, etc...) and it's not terribly uncommon to find one that has had somewhat less than ideal work done on it.
Please let us know what you find out.
- Mike