Alright, let's solve this problem step by step. We have 8119 and 5270 and we're adding them together.

Step 1: We'll start by adding the digits 9 & 0 in column 1 and get 9.

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

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

Step 4: We'll start by adding the digits 8 & 5 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 8119 + 5270 = 13389.

