I was told you have to replace the timing belt every 60,000 miles or five years..I have 24,000 miles and the car is seven years old...

Yes it is! Regardless of mileage, the timing belt and water pump could fail after 7 years. Have these components checked before they fail.

7 or 8 years is about the outside limit depending upon weather conditions.. if you have a timing belt failure,.you run the risk of damaging the engine.