For asymptotes: f(x)=logb(argument) has vertical aymptotes at argument=0
So, n(x) = -ln(x-5) has a vertical asymptote at x =5,
P(x) = cannot go negative, no matter how big a value of -x you put in, so just a horizontal asymptote on that one, no critical value
Critical point is where the derivative of the function is = 0 or undefined. So, the critical value of n(x)=5
I hope that helps!
I'm not sure how to cut and paste the graph in this area, but you can go to desmos graphing calculator (free) and enter your two functions to see it.