My Grandfathers old Browning...

The Browning "Light" 12 has additional machining done to make the gun a bit lighter than the standard model. IIRC my example with a 28" vent-rib barrel weighs about 7-3/4 pounds, although the Cutts probably has added extra weight to yours.

On the topic of the Cutts Compensator, they were equipped with a primitive choke tube system, although the tubes are hard to find. You should be able to replace the barrel with a more recent one (although they are $$$), but I think you will need to replace the recoil system too. If I remember correctly the Cutts guns had a weaker recoil spring and were missing other parts, because the Cutts significantly reduced the force of the barrel's movement. You can find new recoil assemblies on the auction sites and maybe some of the parts sellers like Numrich; they are often sold as rebuild kits.

what action is it?

"Light" is ironic in the gun, I have one and it is far from light in my opinion. It is much lighter then a standard A5 12g. These are big shotguns, stought and durable. Easy to shoot field loads in and handle waterfowl loads well.

In your case, since it is a family gun and your want it to be taken care of, I would contact Browning customer service. They will help you out. If you need a new barrel they have them, keep the original though. Ask about what Zinj spoke of, the reduced spring weights, I had never heard of that before and I would love to hear from them on the subject. They may ask you to send the gun to them, I would go ahead and do it unless you have a great gunsmith friend that you trust. Brownings new barrels have the Invector Plus chokes in them. Personally, I prefer fixed chokes, but I dont try to shoot all game birds with one gun, I use the lack of flexible chokes as an excuse to get more guns.

Browning didn't keep real good track of serial numbers until after WWII. If you tell us what kind of safety it has that can help narrow down the age.

I looked at the serial number list in the back of the Blue Book, but didn't come up with much. Does your serial number have a letter or letters in it?

The Light guns weighed about 10 ounces less than the standard Auto-5. The standard A-5 weighed about 7-1/3 to 8 pounds.

"5 digits and starts with 7" fits the standard A-5 series from about 1926 or 1929 IIRC, well before the introduction of the Lightweight.

Where on the gun does it say lightweight? Just curious.

John

Nice A-5!

IIRC means If I Remember Correctly...

Your shotgun was made between Jun and Dec of 1957.
Yes, you can purchase an Invector or Invector plus barrel and use it in your firearm.
Check Ebay; Midwest Gun Works; BrowningA5; or Barrel Exchange for an extra barrel. You could also try any one of the online firearm auction sites for a barrel. I would recommend the invector plus barrel, it may be easier to get choke tubes. The invector and invector plus choke tubes do not interchange!
Ebay may also have some extra choke tubes for your cutts barrel.

Damn. That gun is in NICE shape!!!!! very very beautiful.

That old humpback will outlast your grandkids. Congratulations on a spectacular gun.

Smoke

Since nobody else mentioned it...
Before any more shooting, please take a few minutes to get familiar with the friction ring set-up and make sure all the parts are there and installed properly.
Nice old A5, congratulations.

Yes you can get a Japanese made barrel - unfortunately it will cost you as much as the shotgun is worth. I would look at having a gunsmith: 1. take the cutts off and restore barrel to factory and 2. give shotgun a through cleaning - they are very tricky to clean inside receiver. Understand the shotgun is designed for shooting upland birds - that is why the 2 3/4" is not a handicap. Use it for that purpose and you will be happy.