Check the box flaps for numbers. The bottom flaps usually have some sort of date.

I might feel more comfortable with shotgun shells due to the relatively low chamber pressures but I would not take the chance with centerfire rifle ammo. A friend had a bad experience with a Sig Sauer bolt action rifle in .30-06 caliber with some old factory ammo from around the late 1970s or early 1980s. Bad detonation in chamber that damaged the chamber, barrel and bolt of the rifle. Luckily he escaped without any injury. Seems the powder in the cartridges had "caked" somehow from storage. I don't think that Sauer offered him any compensation for the damage to the rifle based on the age of the ammo.

It's one thing to play around with a .729 bore shotgun and shells loaded with 18 to 25 grains of powder and 11,000 PSI and quite another to have a mishap with 60 grains of smokeless powder in a bottleneck rifle case, rifled bore just barely the diameter of a solid bullet and 60,000 PSI.

I found this statement on the web but with no citations or attribution:
Ammunition's shelf life is largely predicated on the the conditions under which it is stored. Most manufacturers guarantee that their ammunition will last for at least a decade. That said, ammunition can easily last beyond 10 years if it is stored under ideal conditions. There are countless tales of military surplus ammo being used many decades after it was manufactured.
https://gunpros.com/how-long-does-ammo- ... -store-it/

Let's consider the question from a different perspective---Ammo shortage or not, what are your eyes, fingers and hands worth to you?

If you post clear pictures of the top, front, sides, and back of one of the three boxes, and also the inside flaps for the lot numbers of all three boxes, I will compare the box design with the old Remington catalogs for a range of years manufactured. There is no factory list to decode lot numbers associated with year of manufacture, but a workaround is available.

You will likely need to first load your photos into Microsoft Paint or any photo editor to reduce the width to 635 pixels, then upload them to Imgur, and then use the URLs in your post. Or PM me for my email address and I can do that for you.

call remington. good luck with it

Remington as we once knew it is no longer answering the phone