Okay, we are given 5188 and 635. Let's add them up step by step.

Step 1: We'll start by adding the digits 8 & 5 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 8 & 3 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 6 in column 3 and get 8.

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

So, 5188 + 635 = 5823.

