Okay, we are tasked with adding 5190 and 5003. Let's begin!

Step 1: We'll start by adding the digits 0 & 3 in column 1 and get 3.

Step 2: We'll start by adding the digits 9 & 0 in column 2 and get 9.

Step 3: We'll start by adding the digits 1 & 0 in column 3 and get 1.

Step 4: We'll start by adding the digits 5 & 5 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 5190 + 5003 = 10193.

