The number of ways to arrange a set of 5 different elements is given by the formula for permutations of a set, which is the factorial of the number of elements.

The formula for permutations of $n$ elements is: $n! = n \times (n - 1) \times (n - 2) \times \cdots \times 1$

For 5 elements: $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Thus, the 5 elements can be arranged in 120 different orders.

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:

1. How many ways can 3 elements from the set be chosen and arranged?
2. How does the number of arrangements change with 6 elements instead of 5?
3. What is the difference between permutations and combinations?
4. How would the number of arrangements change if some elements were repeated?
5. How many ways can a set of 5 elements be arranged if order does not matter?

Tip: The factorial function grows very quickly as the number of elements increases!