1. **State the problem:** Simplify the expression $ (x+y)(x-5y) $. 2. **Formula used:** Use the distributive property (also called FOIL for binomials): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the distributive property:** $$ (x+y)(x-5y) = x \cdot x + x \cdot (-5y) + y \cdot x + y \cdot (-5y) $$ 4. **Simplify each term:** $$ = x^2 - 5xy + xy - 5y^2 $$ 5. **Combine like terms:** $$ -5xy + xy = \cancel{-5xy} + \cancel{xy} = -4xy $$ 6. **Final simplified expression:** $$ x^2 - 4xy - 5y^2 $$ This is the expanded and simplified form of the original expression.