depends on who is making the tire.Bridgestone,firestone and Michelin begin to dryrot in less than 2 years. some goodyears do coopers not so much .It also depends on the use like if it is a high performance tire it is more likely to dryrot. There are so many varibles it isn't funny.

As for the 5 year thing that kf6zpl stated some manufacturers less than that.I will let you in on something,If your tire starts dryrotting before the tire reaches full milage, or warrenty end (goodyear is 5 years ,firestone/bridgstone is 4 I think and michelin is 6 i think) whichever comes first you get that tire or those tires replaced at a prorate. for example if you had a goodyear triple tread (80,000 mile treadlife warrenty For 5 years) and 2 years later you notice it is dryrotted or completely worn and you only have 40 k on the tires goodyear will adjust them. meaning they will give you another set at half cost since you got half the milage out of it.