We have numbers 5977 and 1617. Let's start adding them together.

Step 1: We'll start by adding the digits 7 & 7 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

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

Step 3: We'll start by adding the digits 9 & 6 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 1 in column 4 and get 7.

So, 5977 + 1617 = 7594.

