Okay, we are tasked with adding 5684 and 2561. Let's begin!

Step 1: We'll start by adding the digits 4 & 1 in column 1 and get 5.

Step 2: We'll start by adding the digits 8 & 6 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 5 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

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

So, 5684 + 2561 = 8245.

