1. We are asked to evaluate the expression $4^3 - 7(8 + 2) \div 5$. 2. Recall the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 3. First, calculate inside the parentheses: $8 + 2 = 10$. 4. Next, calculate the exponent: $4^3 = 4 \times 4 \times 4 = 64$. 5. Now substitute these values back into the expression: $64 - 7 \times 10 \div 5$. 6. Perform multiplication and division from left to right: - Multiply: $7 \times 10 = 70$. - Divide: $70 \div 5 = 14$. 7. Now the expression is $64 - 14$. 8. Finally, subtract: $64 - 14 = 50$. Therefore, the answer is $50$.