Let's get this math done. We have 78174 and 17037, and we're going to subtract the second number from the first.

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

Step 2: We'll start by subtracting the digit 3 and the borrow 1 from 7 in column 2 and get 3.
3 is the next digit of our result.

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

Step 4: We'll start by subtracting the digit 7 and the borrow 0 from 8 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 1 and the borrow 0 from 7 in column 5 and get 6.
6 is the next digit of our result.

So, 78174 - 17037 = 61137.