Balls are drawn \" without replacement\"
Suppose b red balls, t total balls.
Balls are drawn " without replacement".
So Prob(all 5 red|5 drawn) is
C(b,5)/C(t,5) or equivalently P(b,5)/P(t,5)
and NOT b^5/t^5.
It seems you have simply found that 5129/5892 is a rational approximation for (1/2)^(1/5) which in any case is irrational.
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