If a fair coin is tossed at random 5 independent times, then find the conditional probability of 5 heads relative to the hypothesis that there are at least 4 heads.

Book\\\'s answer: 1/6

My approach:
H=heads
T=tails
conditional probability: p(A|B)=[p(A)np(B)]/p(B)
since they are independent above equation reduces to [p(A)*p(B)]/p(B)

p(5H|x=4H)
=p(5H|1-p(x=3H))
=[p(5H)n(1-p(x=3H))]/p(1-p(x=3H)

I looked up the values of p(5H) and p(x=3H) in the binomial distribution table this is what I got for b(5,.5)
p(5H)=.0312
p(x=3H)=.1875

When I plugged in these numbers in the above equation I got:
[(.0312)(.1875)]/(.1875)=.0312?1/6

Can anyone please help enlighten me on how to get the correct answer.