Okay, we are tasked with adding 5274 and 1516. Let's begin!

Step 1: We'll start by adding the digits 4 & 6 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 1 in column 2 and get 9.

Step 3: We'll start by adding the digits 2 & 5 in column 3 and get 7.

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

So, 5274 + 1516 = 6790.

