1. **State the problem:** We are given a function defined as $f(5x) = \frac{5}{2 + x}$ and asked to find the value of $f(-5)$. 2. **Understand the function:** The function is given in terms of $5x$, so the input to $f$ is $5x$. We want to find $f(-5)$, which means we need to find the value of $x$ such that $5x = -5$. 3. **Find $x$:** Solve for $x$ from $5x = -5$: $$x = \frac{-5}{5} = -1$$ 4. **Substitute $x$ into the function:** Using the formula $f(5x) = \frac{5}{2 + x}$, substitute $x = -1$: $$f(-5) = f(5 \times -1) = \frac{5}{2 + (-1)} = \frac{5}{2 - 1} = \frac{5}{1} = 5$$ 5. **Final answer:** $f(-5) = 5$. Therefore, the correct choice is (D) 5.