1. **State the problem:** Simplify the expression $(-2x + 5y) + (-5x - 7y)$. 2. **Use the distributive property:** Remove parentheses by adding corresponding terms: $$(-2x + 5y) + (-5x - 7y) = -2x + 5y - 5x - 7y$$ 3. **Combine like terms:** Group $x$ terms and $y$ terms: $$(-2x - 5x) + (5y - 7y) = -7x - 2y$$ 4. **Final answer:** $$\boxed{-7x - 2y}$$