Okay, we are tasked with adding 5584 and 3520. Let's begin!

Step 1: We'll start by adding the digits 4 & 0 in column 1 and get 4.

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 5 & 5 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 3 in column 4 and get 9.

So, 5584 + 3520 = 9104.

