1. **State the problem:** We need to subtract the polynomial $(-3m^2 + m + 2)$ from $(-5m^2 - 8)$. This means we calculate $$(-5m^2 - 8) - (-3m^2 + m + 2).$$ 2. **Use the subtraction rule:** When subtracting polynomials, distribute the minus sign to each term in the second polynomial: $$-(-3m^2 + m + 2) = +3m^2 - m - 2.$$ 3. **Rewrite the expression:** $$-5m^2 - 8 + 3m^2 - m - 2.$$ 4. **Combine like terms:** - Combine $-5m^2$ and $3m^2$: $$-5m^2 + 3m^2 = \cancel{-5m^2} + \cancel{3m^2} = -2m^2.$$ - Combine constants $-8$ and $-2$: $$-8 - 2 = -10.$$ - The $-m$ term remains as is. 5. **Write the final polynomial in standard form:** $$-2m^2 - m - 10.$$ **Answer:** $$\boxed{-2m^2 - m - 10}.$$