Okay, we are tasked with adding 804 and 5238. Let's begin!

Step 1: We'll start by adding the digits 4 & 8 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 3 in column 2 and get 4.

Step 3: We'll start by adding the digits 8 & 2 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 0 & 5 in column 4 and get 6.

So, 804 + 5238 = 6042.

