Find all values of x where the function p(x) = \frac{{|x-5|}}{{x-5}} is discontinuous. For each value of x, what is the limit of the function as x approaches a? Note when the limit doesn't exist.

A) x = 5, the limit is 1
B) x = -5, the limit is -1
C) x = 6, the limit doesn't exist
D) x = -6, the limit doesn't exist