Alright, let's solve this problem step by step. We have 2585 and 5259 and we're adding them together.

Step 1: We'll start by adding the digits 5 & 9 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 8 & 5 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 5 & 2 in column 3 and get 8.

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

So, 2585 + 5259 = 7844.

