1. **State the problem:** We are given a piecewise function defined as: $$f(x) = \begin{cases} -2x - 7 & \text{if } x \leq -5 \\ \frac{2}{5}x + 5 & \text{if } x > -5 \end{cases}$$ We need to find the value of $f(5)$. 2. **Identify which piece to use:** Since $5 > -5$, we use the second piece of the function: $$f(x) = \frac{2}{5}x + 5$$ 3. **Substitute $x=5$ into the function:** $$f(5) = \frac{2}{5} \times 5 + 5$$ 4. **Simplify the expression:** $$f(5) = 2 + 5 = 7$$ 5. **Final answer:** $$\boxed{7}$$ This means the value of the function at $x=5$ is 7.