1. \( 131_{5}+424_{5} \)

To add the numbers \( 131_5 \) and \( 424_5 \) in base 5, we can follow the standard addition process, but we need to remember that in base 5, the digits can only be 0, 1, 2, 3, or 4. If the sum of the digits exceeds 4, we carry over to the next column. Let's align the numbers for addition: ``` 131_5 + 424_5 ``` Now, we add column by column from right to left: 1. **Rightmost column**: \( 1 + 4 = 5 \). Since 5 is equal to \( 10_5 \) (which is 0 with a carry of 1), we write down 0 and carry over 1. 2. **Middle column**: \( 3 + 2 + 1 \) (the carry) \( = 6 \). Since 6 is equal to \( 11_5 \) (which is 1 with a carry of 1), we write down 1 and carry over 1. 3. **Leftmost column**: \( 1 + 4 + 1 \) (the carry) \( = 6 \). Again, since 6 is equal to \( 11_5 \) (which is 1 with a carry of 1), we write down 1 and carry over 1. Since we have a carry of 1 left after the last column, we write it down as well. Putting it all together, we have: ``` 131_5 + 424_5 ------- 1100_5 ``` Thus, the sum \( 131_5 + 424_5 = 1100_5 \).