RB60,
The short answer is six to seven years for street tires if they are not used too spiritedly and still have no obvious damage, deterioration or wear. After that it's a matter of how long before one of them fails, usually rather suddenly.
Tires never fully vulcanize when they are manufactured; they continue to change properties as they age, kinda like humans. The internal bonds between layers of rubber and fabric age and lose strength. The rubber itself becomes less elastic, weaker and its traction property decreases.
None of this is usually obvious on the surface. It happens very slowly. If you cut an old tire open and measure its properties against a new tire, the differences will be striking.
Fifteen years for a tire is equivalent to about 25 dog-years
Tom