Okay, we are tasked with adding 5224 and 5369. Let's begin!

Step 1: We'll start by adding the digits 4 & 9 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 2 & 6 in column 2 and get 9.

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

Step 4: We'll start by adding the digits 5 & 5 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 5224 + 5369 = 10593.

