Okay, we are tasked with adding 2564 and 5231. Let's begin!

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

Step 2: We'll start by adding the digits 6 & 3 in column 2 and get 9.

Step 3: We'll start by adding the digits 5 & 2 in column 3 and get 7.

Step 4: We'll start by adding the digits 2 & 5 in column 4 and get 7.

So, 2564 + 5231 = 7795.

