ANSWER:
[tex]f^{-1}(x)=5^x+10[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=\log_5\left(x-10\right)[/tex]To calculate the inverse, we must replace y by x and also x by y, and solve for y, like this:
[tex]\begin{gathered} x=\log _5\left(y-10\right) \\ \\ 5^x=y-10 \\ \\ y=5^x+10 \\ \\ f^{-1}(x)=5^x+10 \end{gathered}[/tex]