Shooting game - a probability question 
In a shooting game, the probability for Jack to hit a target is 0.6.
  Suppose he makes 8 shots, find the probabilities that he can hit the
  target in more than 5 shots.

I find this question in an exercise and do not know how to solve it. I have tried my best but my answer is different from the one in the answer key. Can anyone suggest a clear solution to it?
My trial: (0.6^6)(0.4^2)+(0.6^7)(0.4)+0.6^8
But it is wrong...
(The answer is 0.3154, which is correct to 4 significant figures)

Total shots = n =  8
Success = p = The probability for Jack to hit a target is 0.6
Failure $= q = (1-p) =$ The probability for Jack to NOT Hit a target is $(1- 0.6) = 0.4$
P( He can hit the target in more than 5 shots, i.e. from 6 to 8 ) $= [ P(X = 6) + P(X = 7) + P(X = 8) ] =$ $
 [\binom{8}{6}.(.6)^{6}.(.4)^{8-6} + \binom{8}{7}.(.6)^{7}.(.4)^{8-7} + \binom{8}{8}.(.6)^{8}.(.4)^{8-8} ]$
