1. **State the problem:** Simplify the expression $4(m+5)-2(5m+1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4(m+5) = 4m + 20$$ $$-2(5m+1) = -10m - 2$$ 3. **Rewrite the expression:** $$4m + 20 - 10m - 2$$ 4. **Combine like terms:** Group the terms with $m$ and the constant terms separately. $$4m - 10m + 20 - 2$$ 5. **Simplify:** $$\cancel{4m} - 10m + 20 - 2 = -6m + 18$$ 6. **Final answer:** $$\boxed{-6m + 18}$$