Okay, we are tasked with adding 9576 and 5091. Let's begin!

Step 1: We'll start by adding the digits 6 & 1 in column 1 and get 7.

Step 2: We'll start by adding the digits 7 & 9 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

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

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

So, 9576 + 5091 = 14667.

