Let's solve this addition problem. We have 5077 and 2574, and we need to add them together.

Step 1: We'll start by adding the digits 7 & 4 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 7 in column 2 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 6.

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

So, 5077 + 2574 = 7651.

