Okay, let's tackle this math problem. We're starting with 85907 and subtracting 34378.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 7 in column 1 and get -1.
We add -1 to 10 and get 9 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 0 in column 2 and get -8.
We add -8 to 10 and get 2 as the next digit of the result.

Step 3: We'll start by subtracting the digit 3 and the borrow 1 from 9 in column 3 and get 5.
5 is the next digit of our result.

Step 4: We'll start by subtracting the digit 4 and the borrow 0 from 5 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 8 in column 5 and get 5.
5 is the next digit of our result.

So, 85907 - 34378 = 51529.