We can solve this together! We're beginning with 258096 and removing 5089 from it.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 6 in column 1 and get -3.
We add -3 to 10 and get 7 as the first digit of the result.

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

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

Step 4: We'll start by subtracting the digit 5 and the borrow 0 from 8 in column 4 and get 3.
3 is the next digit of our result.

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

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 2 in column 6 and get 2.
2 is the next digit of our result.

So, 258096 - 5089 = 253007.