Let's break this down. We're going to add 5082 and 9823 together.

Step 1: We'll start by adding the digits 2 & 3 in column 1 and get 5.

Step 2: We'll start by adding the digits 8 & 2 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 8 in column 3 and get 9.

Step 4: We'll start by adding the digits 5 & 9 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 5082 + 9823 = 14905.

