\[\frac{5^{6} \cdot 125}{25^{4}} = \frac{5^{6} \cdot 5^{3}}{\left( 5^{2} \right)^{4}} = \frac{5^{6 + 3}}{5^{2 \cdot 4}} = \frac{5^{9}}{5^{8}} = 5^{9 - 8} =\]
\[= 5\]