We are presented with 5119 and 6583. Let's work out the sum.

Step 1: We'll start by adding the digits 9 & 3 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 8 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 7.

Step 4: We'll start by adding the digits 5 & 6 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 5119 + 6583 = 11702.

