Alright, let's solve this problem step by step. We have 5306 and 7819 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 9 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 0 & 1 in column 2 and get 2.

Step 3: We'll start by adding the digits 3 & 8 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 & 7 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 5306 + 7819 = 13125.

