Okay, let's tackle this math problem. We're starting with 81003 and subtracting 45517.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 3 in column 1 and get -4.
We add -4 to 10 and get 6 as the first digit of the result.

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

Step 3: We'll start by subtracting the digit 5 and the borrow 1 from 0 in column 3 and get -6.
We add -6 to 10 and get 4 as the next digit of the result.

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

Step 5: We'll start by subtracting the digit 4 and the borrow 1 from 8 in column 5 and get 3.
3 is the next digit of our result.

So, 81003 - 45517 = 35486.