\[\frac{5x - 25}{3y + 5}\ :\frac{x^{2} - 25}{6y + 10} =\]
\[= \frac{5x - 25}{3y + 5} \cdot \frac{6y + 10}{x^{2} - 25} =\]
\[= \frac{5(x - 5) \cdot 2(3y + 5)}{(3y + 5)(x - 5)(x + 5)} = \frac{10}{x + 5}.\]