If the knobs are tearing loose then they are shot. The rubber is no longer "live" enough to accept the stretching and it's cracking.
Tires stored in a cool dark place can last for years. But if they are exposed to things like the heat of a garage over successive summers or see a lot of daylight then they'll age fast.
I've got some tires that are put away in the dark in my basement. They are about 7 to 8 years old and while they are showing some signs of hardening they would be rideable. On the other hand my garage gets very warm in the summer. A tire that's about 5 years old mounted on a rim out there is totally shot and is just waiting for me to unmount it and toss it in the garbage at some point when I need that wheel.