Okay, we are given 5781 and 6565. Let's add them up step by step.

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

Step 2: We'll start by adding the digits 8 & 6 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 7 & 5 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 6 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 5781 + 6565 = 12346.

