Okay, we are given 5205 and 3629. Let's add them up step by step.

Step 1: We'll start by adding the digits 5 & 9 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 2 in column 2 and get 3.

Step 3: We'll start by adding the digits 2 & 6 in column 3 and get 8.

Step 4: We'll start by adding the digits 5 & 3 in column 4 and get 8.

So, 5205 + 3629 = 8834.

