1. The given function is $S(p) = \sqrt{500 - 2p} + 5$. 2. For the square root to be defined for real numbers, the radicand (expression inside the square root) must be non-negative: $$500 - 2p \geq 0$$ 3. Solve inequality: $$500 \geq 2p \Rightarrow p \leq \frac{500}{2} = 250$$ 4. Therefore, the domain of $p$ is all values that satisfy: $$p \leq 250$$ 5. Since the square root function outputs real numbers only for non-negative inputs, and no other restrictions are mentioned, $p$ must be less than or equal to 250. 6. The problem's options include various domains; thus, the correct domain is $0 \leq p \leq 250$ assuming $p$ is non-negative (since square root is considered in real numbers and $p > 0$ is indicated). Final answer: The domain of $p$ is $$0 \leq p \leq 250$$.