jmc

If we let $g(x)$ denote the inverse to $f$ then we can evaluate $f$ at $g(x)$ to get $$f(g(x))=4-5g(x).$$Since $g$ is the inverse to $f$, the left side is $x$ and $$x=4-5g(x).$$Solving for $g(x)$, we find $g(x)=\boxed{\frac{4-x}{5}}$.