Let's solve this addition problem. We have 5119 and 5842, and we need to add them together.

Step 1: We'll start by adding the digits 9 & 2 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 4 in column 2 and get 6.

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

Step 4: We'll start by adding the digits 5 & 5 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 5119 + 5842 = 10961.

