Okay, we are tasked with adding 4055 and 5033. Let's begin!

Step 1: We'll start by adding the digits 5 & 3 in column 1 and get 8.

Step 2: We'll start by adding the digits 5 & 3 in column 2 and get 8.

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

Step 4: We'll start by adding the digits 4 & 5 in column 4 and get 9.

So, 4055 + 5033 = 9088.

