Car tires typically last around 50,000 to 60,000 or even 70,000 miles before needing replaced.
Although if you haven't driven 60,000 miles yet and it's been 10 years or almost 10 years the tires should be replaced because of old age.
The rubber on tires start to break down through the years even when the tread on the tires are still good so if your tires at 10 years old or nearing 10 years old the tires are about ready to be replaced before they blowout on you.
Check your tires sidewall and tread area for cracks and if the sidewall has cracks then the tire should be replaced soon.