Okay, let's tackle this math problem. We're starting with 51629 and subtracting 41511.

Step 1: We'll start by subtracting the digit 1 and the borrow 0 from 9 in column 1 and get 8.
8 is the first digit of our result.

Step 2: We'll start by subtracting the digit 1 and the borrow 0 from 2 in column 2 and get 1.
1 is the next digit of our result.

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

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

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

So, 51629 - 41511 = 10118.