We can solve this together! We're beginning with 573977 and removing 55178 from it.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 7 in column 1 and get -1.
We add -1 to 10 and get 9 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 7 in column 2 and get -1.
We add -1 to 10 and get 9 as the next digit of the result.

Step 3: We'll start by subtracting the digit 1 and the borrow 1 from 9 in column 3 and get 7.
7 is the next digit of our result.

Step 4: We'll start by subtracting the digit 5 and the borrow 0 from 3 in column 4 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 5: We'll start by subtracting the digit 5 and the borrow 1 from 7 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, 573977 - 55178 = 518799.