Answer
$-\infty$
Work Step by Step
$x\rightarrow 5^{-}$ means that the values of x are
positive (close to 5) and
being left of 5, slightly less than 5.
For any of these x, the numerator is positive and
the denominator is negative, as it
approaches $0$ from the negative side
So,
$\displaystyle \lim_{x\rightarrow 5^{-}}\frac{x+1}{x-5}=-\infty$
