Divide \( 137 \) by \( 5 \): \(137 \div 5 = 27 \quad \text{(remainder } 2\text{)}\) Divide \( 27 \) by \( 5 \): \(27 \div 5 = 5 \quad \text{(remainder } 2\text{)}\) Divide \( 5 \) by \( 5 \): \(5 \div 5 = 1 \quad \text{(remainder } 0\text{)}\) Divide \( 1 \) by \( 5 \): \(1 \div 5 = 0 \quad \text{(remainder } 1\text{)}\) Now, we collect the remainders in reverse order: \( 1, 0, 2, 2 \). Thus, \( 137 \) in base \( 5 \) is represented as \( 1022_5 \).