Answer
Yes.
Work Step by Step
The above statement can be verified by applying the identity \[\underbrace{{{f}^{-1}}\left( f\left( x \right) \right)}_{\text{LHS}}=\underbrace{x}_{\text{RHS}}\]
By solving the left hand side:
${f}^{-1}(f(x))=$
\[\begin{align}
& \left( \frac{f\left( x \right)+4}{5} \right) \\
& \left( \frac{5x-4+4}{5} \right) \\
& \left( \frac{5x}{5} \right) \\
\end{align}\]
$= (x)$
Thus, the left-hand side of the expression is equal to the right hand side of the expression $=x$
