Let's dive into this subtraction. We'll start with 577545 and subtract 1289 from it.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 5 in column 1 and get -4.
We add -4 to 10 and get 6 as the first digit of the result.

Step 2: We'll start by subtracting the digit 8 and the borrow 1 from 4 in column 2 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 3: We'll start by subtracting the digit 2 and the borrow 1 from 5 in column 3 and get 2.
2 is the next digit of our result.

Step 4: We'll start by subtracting the digit 1 and the borrow 0 from 7 in column 4 and get 6.
6 is the next digit of our result.

Step 5: We'll start by subtracting the digit 0 and the borrow 0 from 7 in column 5 and get 7.
7 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, 577545 - 1289 = 576256.