\[\boxed{\mathbf{759}\mathbf{.}}\]
\[1)\log_{5}625 = \log_{5}5^{4} = 4\]
\[2)\log_{6}216 = \log_{6}6^{3} = 3\]
\[3)\log_{4}\frac{1}{16} = \log_{4}\frac{1}{4^{2}} =\]
\[= \log_{4}4^{- 2} = - 2\]
\[4)\log_{5}\frac{1}{125} = \log_{5}\frac{1}{5^{3}} =\]
\[= \log_{5}5^{- 3} = - 3\]