f(x)= ((2x+3)/(x-5))

we should not confuse f^-1(x) with (f(x))^-1 since

f^-1(x) is the inverse function of f(x)

(f(x))^-1 = 1/f(x)

in our case we have

(f(x))^-1 = 1/f(x) = 1/((2x+3)/(x-5))

(f(x))^-1 = (x-5)/(2x+3)