Okay, we are tasked with adding 5019 and 4525. Let's begin!

Step 1: We'll start by adding the digits 9 & 5 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 1 & 2 in column 2 and get 4.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 5.

Step 4: We'll start by adding the digits 5 & 4 in column 4 and get 9.

So, 5019 + 4525 = 9544.

