Okay, we are tasked with adding 4879 and 5830. Let's begin!

Step 1: We'll start by adding the digits 9 & 0 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 3 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 8 & 8 in column 3 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

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

So, 4879 + 5830 = 10709.

