... ... I had a case where the tire was perhaps 10 years old and it had dry rotted in that spot and also cracked. When I wore through a previous Schwalbe, I put on this (old) tire and it failed about 10 miles later. I took that not so much on Schwalbe but more that I had saved the tire for too long.
I think it depends on how it is stored, both temperature and humidity.
I think both tires on my light touring bike right now are over a decade old. One of them is a Schwalbe XR which I think has been out of production for at least a decade, I put that tire on it when I built it up eight years ago. The other is a Hutchinson Globetrotter that I think I bought over a decade ago. I think the Globetrotter does not have much life left, about two thirds of the tread is gone. I used that bike for my tour last summer, but for the tour I put a Mondial on the rear instead of the Globetrotter, which went back on it when I got home.
Now that I think about it, I think I put the tires that are on my rando bike on it in early or mid 2017. So, those are at about eight years, the rear tire tread is almost all gone. I was thinking I should take that tire off and use it as a spare tire, it still has several hundred miles of rubber on it and has a folding bead.