Probability of landing 5 heads in a row = 1/32

Let the number of coin flips required to land 5 heads in a row be 'a'

a = 5×(1/32){5 heads in a row} + (a+1)(1/2){first flip was tails} + (a + 2)(1/4){2 flips wasted on tails} + (a + 3)(1/8){3 flips wasted on tails} + (a + 4)(1/16){4 flips wasted on tails} + (a + 5)(1/32){5 flips wasted on tails}

on simplifying

a = **62.** So we need 62 tosses on average to get 5 heads in a row.