Answer
$f^{-1}(x)=\sqrt[3]{x}+5$
Work Step by Step
$f(x)=(x-5)^{3}$
Replace $f(x)$ with $y$:
$y=(x-5)^{3}$
Interchange $x$ and $y$:
$x=(y-5)^{3}$
Solve for $y$. Start by taking the cubic root of both sides:
$\sqrt[3]{x}=\sqrt[3]{(y-5)^{3}}$
$\sqrt[3]{x}=y-5$
Take the $-5$ to the left side:
$\sqrt[3]{x}+5=y$
Replace $y$ with $f^{-1}(x)$:
$f^{-1}(x)=\sqrt[3]{x}+5$