Answer
$log_{5}(y^{4}-7y^{3})$
Work Step by Step
We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{5}y^{3}+log_{5}(y-7)=log_{5}(y^{3}\times (y-7))=log_{5}(y^{4}-7y^{3})$.