1. **State the problem:** Simplify the expression $5 - 7 + 2(3 - 8)$. 2. **Apply the order of operations:** First, simplify inside the parentheses. 3. Calculate $3 - 8 = -5$. 4. Substitute back: $5 - 7 + 2(-5)$. 5. Multiply: $2 \times (-5) = -10$. 6. Now the expression is $5 - 7 - 10$. 7. Perform subtraction from left to right: $5 - 7 = -2$. 8. Then $-2 - 10 = -12$. 9. **Final answer:** $-12$.