Alright, let's solve this problem step by step. We have 2509 and 5127 and we're adding them together.

Step 1: We'll start by adding the digits 9 & 7 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 2 in column 2 and get 3.

Step 3: We'll start by adding the digits 5 & 1 in column 3 and get 6.

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

So, 2509 + 5127 = 7636.

