Okay, we are given 8674 and 5129. Let's add them up step by step.

Step 1: We'll start by adding the digits 4 & 9 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 7 & 2 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 6 & 1 in column 3 and get 8.

Step 4: We'll start by adding the digits 8 & 5 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 8674 + 5129 = 13803.

