Alright, let's solve this problem step by step. We have 1003 and 5563 and we're adding them together.

Step 1: We'll start by adding the digits 3 & 3 in column 1 and get 6.

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

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 5.

Step 4: We'll start by adding the digits 1 & 5 in column 4 and get 6.

So, 1003 + 5563 = 6566.

