Tyres do degrade with time.
How long depends on exposure to UV light, temperature mechanical stress etc.
I'd agree you should try them carefully and see how they are.
Personally I strongly disagree with the suggestion that you should keep them until they wear out!
I bought a car built 9 years previously, new tyres, 6,000 miles, loads of tread.
Handling was poor, dangerous in the wet.
Best money I ever spent was 4 new tyres.
They are the only point of contact with you and the road!