\(413_7\) to base 5 convert first to base 10 \(417_7 = 4 \times 7^2 + 1 \times 7^1 + 3 \times 7^0\) = 4 \times 49 + 1 \times 7 + 3 \times 1 = 196 + 7 + 3 = \(206_{10}\) convert this result to base 5 5 206 5 41R1 5 8R1 5 1R3 0R1 \(∴ 413_7 = 1311_5\)