To find how many different 5-digit numbers can be formed by arranging the digits 1, 2, 3, 4, and 5, we need to calculate the number of permutations of these five digits.

A permutation is an arrangement of all elements of a set in a specific order. The number of permutations of $n$ distinct objects is given by $n!$ (n factorial).

For this problem, there are 5 distinct digits (1, 2, 3, 4, 5). The number of different 5-digit numbers that can be formed is:

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Thus, 120 different 5-digit numbers can be formed by arranging the digits 1, 2, 3, 4, and 5.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How many different 4-digit numbers can be formed using the digits 1, 2, 3, and 4?
2. How many different 5-digit numbers can be formed if repetition of digits is allowed?
3. If the digits 1, 2, 3, 4, and 5 are arranged in a circle, how many different arrangements are possible?
4. What is the probability of randomly arranging the digits 1, 2, 3, 4, and 5 and getting a number greater than 30,000?
5. How many even 5-digit numbers can be formed by arranging the digits 1, 2, 3, 4, and 5?

Tip: When calculating permutations or combinations, first determine if the order of arrangement matters, which will guide you to the correct formula.