We can solve this together! We're beginning with 55572 and removing 34037 from it.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 2 in column 1 and get -5.
We add -5 to 10 and get 5 as the first digit of the result.

Step 2: We'll start by subtracting the digit 3 and the borrow 1 from 7 in column 2 and get 3.
3 is the next digit of our result.

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

Step 4: We'll start by subtracting the digit 4 and the borrow 0 from 5 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 5 in column 5 and get 2.
2 is the next digit of our result.

So, 55572 - 34037 = 21535.