Answer
Domain: $ x\geq 0$
Range: $y\leq 0$
Work Step by Step
Given \begin{equation}
f(x)=-5 \sqrt{x}.
\end{equation} The radicand of a radical function must be positive. This means that we must have $x\geq 0$. Also, we see that the function's value must satisfy $y\leq 0$ because $$(\sqrt x\geq 0)\Rightarrow (5\sqrt x\geq 0)\Rightarrow (-5\sqrt x\leq 0)\Rightarrow (y\leq 0).$$ Therefore we have: \begin{equation}
\begin{aligned}
\textbf{Domain :}\quad & x\geq 0\\
\textbf{Range :}\quad & y\leq 0\\\\
\end{aligned}
\end{equation}
