Looking for Solution Feedback

Could someone please review this problem that I have attempted to simplify. I'm not sure but I believe that I have completed everything correctly.

$\displaystyle log_{5}\frac{5^{-2x} (25)^y}{\sqrt{125^x}}$

$\displaystyle \Rightarrow\log_{5}5^{-2x}+\log_{5}25^{y}-\log_{5}\sqrt{125^{x}}$

$\displaystyle \Rightarrow\text{-}2x\log_{5}5+2y\log_{5}5-\frac{3x}{2}\log_{5}5$

$\displaystyle \Rightarrow\text{-}2x+2y-\frac{3x}{2}$

$\displaystyle \Rightarrow\frac{-7x}{2}+2y$

Any feedback is appreciated.