The set of all integers that are multiples of 5 can be defined in set-builder notation as:

$S = \{ x \in \mathbb{Z} \mid x = 5k, \, k \in \mathbb{Z} \}$

Where:

• $x \in \mathbb{Z}$ means $x$ is an integer.
• $x = 5k$ means $x$ is a multiple of 5.
• $k \in \mathbb{Z}$ means $k$ is any integer.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the set of multiples of 3 be written in set-builder notation?
2. What is the intersection of the set of multiples of 5 and the set of multiples of 2?
3. How do we write the set of even integers in set-builder notation?
4. What is the union of the set of multiples of 5 and multiples of 7?
5. Can the set of multiples of 5 be a finite set? Why or why not?

Tip: Set-builder notation helps describe sets concisely by using conditions or rules to define membership.