We can solve this together! We're beginning with 96437 and removing 89419 from it.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 7 in column 1 and get -2.
We add -2 to 10 and get 8 as the first digit of the result.

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

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

Step 4: We'll start by subtracting the digit 9 and the borrow 0 from 6 in column 4 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 5: We'll start by subtracting the digit 8 and the borrow 1 from 9 in column 5 and get 0.
0 is the next digit of our result.

So, 96437 - 89419 = 7018.