Here is the number line representing the solution set for $|x| \neq 5$:

• All points on the number line are included except for $x = 5$ and $x = -5$, which are excluded (shown with open red circles).

Would you like further details or explanations? Here are a few related questions:

1. How would the solution change if the inequality was $|x| \leq 5$?
2. What does the expression $|x| = 5$ represent geometrically?
3. How do absolute value inequalities differ from standard inequalities?
4. Can you explain how to solve $|x| \neq a$ for a general value $a$?
5. How can this concept be applied to real-world scenarios involving distances?

Tip: When dealing with absolute value inequalities, it's often useful to visualize them on a number line to understand the range of possible solutions.