1. **State the problem:** Simplify the expression $5y + (y-2)(y+8)$. 2. **Recall the formula:** Use the distributive property (FOIL) to expand $(y-2)(y+8)$. 3. **Expand:** $$ (y-2)(y+8) = y \cdot y + y \cdot 8 - 2 \cdot y - 2 \cdot 8 = y^2 + 8y - 2y - 16 $$ 4. **Simplify inside the parentheses:** $$ y^2 + (8y - 2y) - 16 = y^2 + 6y - 16 $$ 5. **Substitute back:** $$ 5y + y^2 + 6y - 16 $$ 6. **Combine like terms:** $$ y^2 + (5y + 6y) - 16 = y^2 + 11y - 16 $$ 7. **Final answer:** $$ y^2 + 11y - 16 $$