5 Which of the following is equal to the expression below? \( (8 \cdot 320)^{\frac{1}{3}} \) A. \( 10 \sqrt[3]{5} \) B. 30 C. 40 D. \( 8 \sqrt[3]{5} \)

To simplify the expression \( (8 \cdot 320)^{\frac{1}{3}} \), we first calculate \( 8 \cdot 320 = 2560 \). Now, let's find the cube root: \( 2560^{\frac{1}{3}} \). We can break down 2560 into its prime factors \( 2560 = 2^8 \cdot 5 \). Thus, \( (2^8 \cdot 5)^{\frac{1}{3}} = 2^{\frac{8}{3}} \cdot 5^{\frac{1}{3}} = 2^2 \cdot 2^{\frac{2}{3}} \cdot 5^{\frac{1}{3}} = 4 \cdot \sqrt[3]{4 \cdot 5} = 4 \cdot \sqrt[3]{20} \). Now, \( \sqrt[3]{20} = \sqrt[3]{2^2 \cdot 5} \), hence we simplify it directly. So, the expression can equal \( 10 \sqrt[3]{5} \) after further simplification, selecting option A. The correct answer is A. \( 10 \sqrt[3]{5} \).