Let's dive into this subtraction. We'll start with 62629 and subtract 59041 from it.

Step 1: We'll start by subtracting the digit 1 and the borrow 0 from 9 in column 1 and get 8.
8 is the first digit of our result.

Step 2: We'll start by subtracting the digit 4 and the borrow 0 from 2 in column 2 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 3: We'll start by subtracting the digit 0 and the borrow 1 from 6 in column 3 and get 5.
5 is the next digit of our result.

Step 4: We'll start by subtracting the digit 9 and the borrow 0 from 2 in column 4 and get -7.
We add -7 to 10 and get 3 as the next digit of the result.

Step 5: We'll start by subtracting the digit 5 and the borrow 1 from 6 in column 5 and get 0.
0 is the next digit of our result.

So, 62629 - 59041 = 3588.