Okay, let's tackle this math problem. We're starting with 51627 and subtracting 35080.

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

Step 2: We'll start by subtracting the digit 8 and the borrow 0 from 2 in column 2 and get -6.
We add -6 to 10 and get 4 as the next digit of the result.

Step 3: We'll start by subtracting the digit 0 and the borrow 1 from 6 in column 3 and get 5.
5 is the next digit of our result.

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

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

So, 51627 - 35080 = 16547.