No problem, let's work through this together. We're starting with 557391 and are subtracting 42209 from it.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 1 in column 1 and get -8.
We add -8 to 10 and get 2 as the first digit of the result.

Step 2: We'll start by subtracting the digit 0 and the borrow 1 from 9 in column 2 and get 8.
8 is the next digit of our result.

Step 3: We'll start by subtracting the digit 2 and the borrow 0 from 3 in column 3 and get 1.
1 is the next digit of our result.

Step 4: We'll start by subtracting the digit 2 and the borrow 0 from 7 in column 4 and get 5.
5 is the next digit of our result.

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

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

So, 557391 - 42209 = 515182.