We can solve this together! We're beginning with 79581 and removing 39340 from it.

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

Step 2: We'll start by subtracting the digit 4 and the borrow 0 from 8 in column 2 and get 4.
4 is the next digit of our result.

Step 3: We'll start by subtracting the digit 3 and the borrow 0 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 9 and the borrow 0 from 9 in column 4 and get 0.
0 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 7 in column 5 and get 4.
4 is the next digit of our result.

So, 79581 - 39340 = 40241.