Probability of 5 out of 12 Students Participating

In a certain class, there are 12 students who can choose to participate in a math competition. Each student can decide to either participate or not participate independently of each other. If the probability that a given student decides to participate is $p$, what is the probability that exactly 5 students will participate in the competition?

Assume $p$ is known to be 0.7. Use the binomial probability formula, which is given as:

$$ P(X = k) = {n rack k} p^k (1-p)^{n-k} $$

where $n$ is the total number of trials (students), $k$ is the number of successes (students who participate), and ${n rack k}$ is the binomial coefficient.