Alright, let's solve this problem step by step. We have 82580 and 72519, and we're subtracting the second number from the first.

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

Step 2: We'll start by subtracting the digit 1 and the borrow 1 from 8 in column 2 and get 6.
6 is the next digit of our result.

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

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

Step 5: We'll start by subtracting the digit 7 and the borrow 0 from 8 in column 5 and get 1.
1 is the next digit of our result.

So, 82580 - 72519 = 10061.