Call the number of miles Peter rode on the first day is a

We have:

The sum of five days Peter rode is:

a + ( a + 10 ) + ( a + 10 + 10 ) + ( a + 10 + 10 + 10 ) + ( a + 10 + 10 + 10 + 10 ) = 5a + 100 = 500 (miles)

=> 5a = 400

=> a = 80 ( miles)

=> a + 10 + 10 + 10 + 10 = 120 ( miles)

So he rode 120 miles on just the fifth day.