Answer
$-7$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to 4} \dfrac{\sqrt x+5}{\sqrt x-5}=\dfrac{\lim_\limits{x\to 4} \sqrt x+5}{\lim_\limits{x\to 4} x-5}$
or, $=\dfrac{7}{-1}$
or, $=-7$
