There is a date code on the sidewall (usually just on one side) required by the DOT.
It starts off with the letters DOT .
Then a group of letters and numbers , these are a code for where it was built.
Then 4 numbers , these are the date code for when the tire was manufactured.
It will only be 3 numbers if it was from 2000-2009 , the first two will still be the week.
(On a tire I just looked at they are 2514 , the 25 is the week of the year and the 14 is the year.)
So that tire was made in the 25th week of 2014 !
Tires experts say any over 7-10 years old should be replaced regardless of the tread depth .
The rubber compounds will break down (even if it was just sitting on a shelf at the store) this might not show on the outside either.
Also , if the sidewalls show cracking , they are near the end of life too.
They "might" self destruct.
Now all this said , I have some old tires on my rig (almost 20 yo) and I still haven't replaced them , BUT I don't take the rig very far (usually under 25 miles at a time )OR go very fast ( I try to keep under 45mph).
I do plan on getting new ones but am working on getting a set of 16" wheels first (they're 16.5" now).
It's hard to find 16.5" tires that were made in the last couple of years. So I'm going to switch to 16" .........