Answer
There is a discontinuity when $a=5$.
Thus, the limit of this function does not exist.
Work Step by Step
We are given $p(x)=\frac{|5-x|}{x-5}$
This rational function is discontinuous wherever the denominator is zero.
There is a discontinuity when $a=5$
For $x\lt 5 \rightarrow \frac{|5-x|}{x-5}=\frac{(5-x)}{-(x-5)}=-1$
For $x\gt 5 \rightarrow \frac{|5-x|}{x-5}=\frac{-(5-x)}{x-5}=1$
Thus, the limit of this function does not exist.