Okay, we are tasked with adding 5194 and 5298. Let's begin!

Step 1: We'll start by adding the digits 4 & 8 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 9 in column 2 and get 19.
We'll write down the last digit 9 and carry the 1 to the next column.

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

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

So, 5194 + 5298 = 10492.

