1. The problem is to find the value of the binomial coefficient $\binom{2}{5}$. 2. The binomial coefficient $\binom{n}{k}$ is defined as the number of ways to choose $k$ elements from a set of $n$ elements without regard to order. 3. The formula for the binomial coefficient is: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ where $n!$ denotes the factorial of $n$. 4. Important rule: If $k > n$, then $\binom{n}{k} = 0$ because you cannot choose more elements than are available. 5. In this problem, $n=2$ and $k=5$. Since $5 > 2$, by the rule above: $$\binom{2}{5} = 0$$ 6. Therefore, the answer is 0.