A particular number is written as $132$ in radix-4 representation. The same number in radix-5 representation is __________.

To convert the number $(132)_4$ to radix-5 representation, first convert it to base-10 (decimal):

Next, convert $30_{10}$ to radix-5 by successive division by $5$:

• $30 \div 5 = 6$ with remainder $0$ (least significant digit)

• $6 \div 5 = 1$ with remainder $1$

• $1 \div 5 = 0$ with remainder $1$ (most significant digit)

Reading the remainders from most significant to least significant gives:

Hence, the number in radix-5 representation is 110.