1. **Problem stated:** Simplify the expression $$\frac{x^2-25}{x^2+5x}\div\frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite division as multiplication by the reciprocal:** $$\frac{x^2-25}{x^2+5x}\cdot\frac{5x-15}{xy+6x-5y-30}$$. 3. **Factor every polynomial:** $$x^2-25=(x-5)(x+5),\quad x^2+5x=x(x+5),\quad 5x-15=5(x-3),$$ $$xy+6x-5y-30=y(x-5)+6(x-5)=(x-5)(y+6).$$ 4. **Substitute the factored forms:** $$\frac{(x-5)(x+5)}{x(x+5)}\cdot\frac{5(x-3)}{(x-5)(y+6)}$$. 5. **Cancel common factors carefully:** $$\frac{\cancel{(x-5)}\cancel{(x+5)}}{x\cancel{(x+5)}}\cdot\frac{5(x-3)}{\cancel{(x-5)}(y+6)}=\frac{5(x-3)}{x(y+6)}$$. 6. **Final answer:** $$\boxed{\frac{5(x-3)}{x(y+6)}}$$.