Alright, let's solve this problem step by step. We have 5038 and 1415 and we're adding them together.

Step 1: We'll start by adding the digits 8 & 5 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 3 & 1 in column 2 and get 5.

Step 3: We'll start by adding the digits 0 & 4 in column 3 and get 4.

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

So, 5038 + 1415 = 6453.

