OK, let's do this. We've got 5059 and 5979 and we're adding them all together.

Step 1: We'll start by adding the digits 9 & 9 in column 1 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 5 & 7 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 9 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

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

So, 5059 + 5979 = 11038.

