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

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