We can solve this together! We're beginning with 512517 and removing 99020 from it.

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

Step 2: We'll start by subtracting the digit 2 and the borrow 0 from 1 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 0 and the borrow 1 from 5 in column 3 and get 4.
4 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 9 and the borrow 1 from 1 in column 5 and get -9.
We add -9 to 10 and get 1 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 5 in column 6 and get 4.
4 is the next digit of our result.

So, 512517 - 99020 = 413497.