smc

${\log }_5\frac{(125)(625)}{25}$ can be simplified to ${\log }_5(125)(25)$ since $25^2=625$. $125=5^3$ and $5^2=25$ so ${\log }_5{5}^5$ would be the simplest form. In ${\log }_5{5}^5$, $5^x=5^5$. Therefore, $x=5$ and the answer is $\boxed{5}$.