3 spare tires are needed. This works if you rotate the tires every 5,000 miles.
Tire A, B, C, D (and spare is E F G)
first 5,000 miles you use tire A B C D
second 5000 miles you use tire B C D E
third 5000 miles you use A E F G
Each tires is used no more than twice (10,000 miles).