5=5m+b passes through (5,5) where m=slope and b is y intercept. y=x (b=0 and m=1) fits. Also y=5x-20 (m=5, b=-20). f(x)=x is its own inverse.
Inverse of f(x) is found by putting y=f(x)=5x+5; 5x=y-5; x=y/5-1. Put g(y)=y/5-1, so g(y) is the inverse of f(x) and we can write f^-1(x)=x/5-1 as the inverse function. The inverse of f(x)=5x-20 is f^-1(x)=x/5+4 which passes through (5,5).