Okay, we are tasked with adding 5401 and 8774. Let's begin!

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

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

Step 3: We'll start by adding the digits 4 & 7 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 8 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 5401 + 8774 = 14175.

