If he shoots at the target 5 the probability of hitting the target all 5 times is 0.6^5.

If he shoots at it 6 times the probability of haviung exactly 5 hits is C(6,5) x 0.6^5 x 0.4^1

If he shoots 7 times the probability of hitting it 5 times is C(7,5) x 0.6^5 0.4^2

In general if shooting N times the probability of hitting it 5 times is C(N,5) x 0.6^5 x 0.4^(N-5). This is the binomial probability formula. So try some values of N and find what value leads to a result >0.25.