x = 2 is the vertical asymptote
y = 5 is the horizontal asymptote
the vertical asymptote is when it is undefined, or when the denominator is 0. this is when x = 2.
to find the horizontal asymptote, we need to find the value y can never be. notice 1/(x-2) is never 0, so when y = 5, that value has to be 0, but this is not possible, so y = 5 is the vertical asymptote.