Okay, we are tasked with adding 5378 and 6703. Let's begin!

Step 1: We'll start by adding the digits 8 & 3 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 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 3 & 7 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 & 6 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 5378 + 6703 = 12081.

