Identify parameters

We use the Binomial Distribution formula where $n=8$ (total tosses) and $k=5$ (target successes). Since the probability of a tail $p=0.5$ and head $q=0.5$, the formula simplifies as $p^k q^{n-k} = (0.5)^8$.

$P(X=5) = \binom{8}{5} (0.5)^8$

Calculate the binomial coefficient

The number of ways to choose 5 tails out of 8 tosses is calculated as $\binom{8}{5} = \frac{8!}{5!3!}$.

$\binom{8}{5} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$

Final computation

Multiply the combination by the probability value: $56 \times \frac{1}{2^8} = \frac{56}{256}$.

$P(X=5) = \frac{56}{256} = 0.21875 \approx 0.22$