Okay, we are tasked with adding 5018 and 9257. Let's begin!

Step 1: We'll start by adding the digits 8 & 7 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 5 in column 2 and get 7.

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

Step 4: We'll start by adding the digits 5 & 9 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 5018 + 9257 = 14275.

