1. The problem asks to find the derivative of the function $g(x) = \sin(x)$ and then evaluate this derivative at $x = 5$. 2. Recall that the derivative of $\sin(x)$ with respect to $x$ is $\cos(x)$. So, $$g'(x) = \frac{d}{dx} \sin(x) = \cos(x)$$ 3. To find $g'(5)$, substitute $x = 5$ into $g'(x)$: $$g'(5) = \cos(5)$$ The value of $\cos(5)$ is a specific real number (approximately $0.2837$) but we leave the answer as $\cos(5)$ for exactness. Final answers: $g'(x) = \cos(x)$ $g'(5) = \cos(5)$