Okay, we are tasked with adding 5198 and 9839. Let's begin!

Step 1: We'll start by adding the digits 8 & 9 in column 1 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 3 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 8 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 9 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 5198 + 9839 = 15037.

