Explanation

To add these numbers, convert them to base 10, add, and then convert back to base 5:

(34)₅ = 3 × 5¹ + 4 × 5⁰ = 15 + 4 = 19

(44)₅ = 4 × 5¹ + 4 × 5⁰ = 20 + 4 = 24

Add the base 10 equivalents:

19 + 24 = 43

Convert the sum back to base 5:

43 = 3 × 5² + 1 × 5¹ + 3 × 5⁰

= (133)₅