$$\begin{array}{|c|c|c|c|} \hline f(5) & g(5) & f'(5) & g'(5) \\ \hline -1 & 2 & 5 & -2 \\ \hline \end{array}$$

The table above gives values for the functions $f$ and $g$ and their derivatives at $x=5$. Let $k$ be the function given by $k(x)=\dfrac{f(x)}{g(x)}$, where $g(x)\neq 0$. What is the value of $k'(5)$ ?

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$$k(x)=\frac{f(x)}{g(x)}$$ $$k'(x)=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}$$ $$k'(5)=\frac{g(5)f'(5)-f(5)g'(5)}{(g(5))^2}$$ $$k'(5)=\frac{(2)(5)-(-1)(-2)}{(2)^2}$$ $$k'(5)=\frac{8}{4}$$ $$k'(5)= \boxed{2}$$