There are three tyres. Each of them has to travel 1000 miles. So a total of 3000 tyre miles is to be divided among 5 tyres. Thus each tyre will be used 600 miles each in the optimum solution.
Let us see one solution. There may be more.
There are tyres a, b, c, d and e.
first 200 miles: tyres a, b , c
next 200 miles: c, d, e
next 200 miles: a, b, d
next 200 miles: a. c e
next 200 miles: b d e
Thus there are totally 8 tyre changes, 4 halts in between.