I just love the A5, have three, 12-16-20. You don't have to push the barrel all the way in, that spring is a bit rough for an old guy like me with nerve damage, just enough to "take the pressure" off the end, just a tick till it moves.
The stock could be a bit of a challenge if it has not been off in a while, if it does fight you go slow, stay away from prying on anything and you will get it. Inside they are IMHO not that hard, There is rougher things out there. I would replace the recoil spring as a given, as to the friction rings and spring, they can and do get weak like any other spring, never seen one bust however. Pretty easy way to tell. Set the rings up for heavy loads, shoot some softer target loads in it, if the gun will cycle fine, you need a new spring.....or you put way too much oil where the rings ride.
There is a little wooden dowel that holds in the recoil spring, as I understand things this was always wood, and if it is a normal roll pin, or plastic it has been replaced. I also want to say they all came with the setup instructions on the inside of the hand guard. If the gun was ever sent in it was SOP to remove that sticker as it could interfere with the action of the gun. If it is there bonus.
Getting the pin out so you can take the bolt apart can also be a bear, I busted up two 16th punches trying to get mine out. If it does not want to go it may not just go, you might need to take it in. My 20 is this way and I can't get the sucker apart. Suggestion on the shotgun forum was to just ride it out, not an area that gets that dirty and just live with it. That sticks in my craw, so mine went to a smith to get it out. They never tend to believe you and he busted up three of his punches before he made something to put in the gun so he could put it in a press. Would have lost my cookies if he busted that 20. It is a first year for the new 20 in 1957 IIRC.
They are fantastic fun guns, and they are the go to when people come out to bust flying orange things. Great fun.
Yours does look like it needs a good cleaning, get her up and going, they are fantastic IMHO, but many people can't stand them as being too complex. There is no doubt more is going on vs a new Benelli.