Answer
$log_{5}x-4log_{5}y$
Work Step by Step
We know that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{5}\frac{x}{y^{4}}=log_{5}x-log_{5}y^{4}$.
We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number).
Therefore, $log_{5}x-log_{5}y^{4}=log_{5}x-4log_{5}y$.