Since the remainder of dividing $n$ by 3 is 2, we can write $n = 3k + 2$ for some integer $k$.
Now, let's consider $5n$.
We have $5n = 5(3k + 2) = 15k + 10$.
The remainder of dividing $15k + 10$ by 3 is the same as the remainder of dividing $10$ by 3, which is $\boxed{1}$.
The answer is: 1
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If the remainder of dividing $n$ by 3 is 2, what is the remainder when $5n$ is divided by 3?

### Answer:
