1. **State the problem:** Simplify the expression $-3(x + y) + 5(x - y)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$-3(x + y) = -3x - 3y$$ $$5(x - y) = 5x - 5y$$ 3. **Rewrite the expression:** $$-3x - 3y + 5x - 5y$$ 4. **Combine like terms:** Group the $x$ terms and the $y$ terms. $$(-3x + 5x) + (-3y - 5y) = 2x - 8y$$ 5. **Final answer:** $$2x - 8y$$