The probability of throwing a 5 is given as 0.75. Therefore, the probability of not throwing a 5 is:

\(1 - 0.75 = 0.25\)

We need to find the probability of getting at least 8 fives in 10 throws. This is a binomial probability problem where:

\(n = 10, \ p = 0.75\)

The probability of getting exactly \(r\) fives is given by the binomial formula:

\(P(X = r) = \binom{n}{r} p^r (1-p)^{n-r}\)

We need to calculate \(P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)\).

Calculating each term:

\(P(X = 8) = \binom{10}{8} (0.75)^8 (0.25)^2\)

\(P(X = 9) = \binom{10}{9} (0.75)^9 (0.25)^1\)

\(P(X = 10) = \binom{10}{10} (0.75)^{10}\)

Substituting the values:

\(P(X = 8) = 45 \times (0.75)^8 \times (0.25)^2\)

\(P(X = 9) = 10 \times (0.75)^9 \times (0.25)\)

\(P(X = 10) = 1 \times (0.75)^{10}\)

Summing these probabilities gives:

\(P(X \geq 8) = 0.526\)