Which of the following numbers is different from the rest?
$$13,17,23,27,29$$

Let's analyze the mathematical properties of the given numbers:
* $13,17,23,$ and $29$ are all prime numbers because they have no positive divisors other than $1$ and themselves.
* $27$ is a composite number since it can be factored as $3\times 3\times 3=27$.

Therefore, $27$ is different from the rest.