1. **State the problem:** Simplify the expression $5(x+y)-2(x-y)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$5(x+y) = 5x + 5y$$ $$-2(x-y) = -2x + 2y$$ 3. **Rewrite the expression:** $$5x + 5y - 2x + 2y$$ 4. **Combine like terms:** Group the $x$ terms and the $y$ terms. $$ (5x - 2x) + (5y + 2y) = 3x + 7y$$ 5. **Final answer:** $$3x + 7y$$ This is the simplified form of the original expression.