Alright, let's solve this problem step by step. We have 5022 and 1583 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 3 in column 1 and get 5.

Step 2: We'll start by adding the digits 2 & 8 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 6.

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

So, 5022 + 1583 = 6605.

