Okay, we are tasked with adding 5626 and 6909. Let's begin!

Step 1: We'll start by adding the digits 6 & 9 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

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

Step 3: We'll start by adding the digits 6 & 9 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 6 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 5626 + 6909 = 12535.

