Let's break this down. We're going to add 177 and 5782 together.

Step 1: We'll start by adding the digits 7 & 2 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 8 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 1 & 7 in column 3 and get 9.

Step 4: We'll start by adding the digits 0 & 5 in column 4 and get 5.

So, 177 + 5782 = 5959.

