Okay, we are given 5259 and 586. Let's add them up step by step.

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

Step 2: We'll start by adding the digits 5 & 8 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 2 & 5 in column 3 and get 8.

Step 4: We'll start by adding the digits 5 & 0 in column 4 and get 5.

So, 5259 + 586 = 5845.

