Let's break this down. We're going to add 5565 and 476 together.

Step 1: We'll start by adding the digits 5 & 6 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 6 & 7 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 5 & 4 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 5 & 0 in column 4 and get 6.

So, 5565 + 476 = 6041.

