Alright, let's solve this problem step by step. We have 9966 and 5755 and we're adding them together.

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

Step 3: We'll start by adding the digits 9 & 7 in column 3 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 9 & 5 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 9966 + 5755 = 15721.

