Replace the variable y with x and x with y.
[tex]x=5^{y+4}[/tex]Simplify the equation for y.
[tex]\begin{gathered} \ln (x)=\ln (5^{y+4}) \\ \ln x=(y+4)\ln 5 \\ y+4=\frac{\ln x}{\ln 5} \\ y=\frac{\ln x}{\ln 5}-4 \end{gathered}[/tex]So inverse for the function is,
[tex]y=\frac{\ln x}{\ln5}-4[/tex]