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The question asks to solve the inequality:

\[
(x + 1)(x - 5) < 0, \quad x \in \mathbb{R}
\]

and determine which range of \( x \) satisfies the inequality.

### Steps to solve:

1. **Find the critical points**: 
   Solve \((x + 1)(x - 5) = 0\).
   - \( x + 1 = 0 \Rightarrow x = -1 \)
   - \( x - 5 = 0 \Rightarrow x = 5 \)

   So the critical points are \( x = -1 \) and \( x = 5 \).

2. **Determine the sign of the expression**: 
   The expression \((x + 1)(x - 5)\) changes signs at these critical points. We can check the sign of the expression in three intervals:
   - For \( x < -1 \): Choose \( x = -2 \), \((x + 1)(x - 5) = (-2 + 1)(-2 - 5) = (-1)(-7) = 7 > 0\).
   - For \( -1 < x < 5 \): Choose \( x = 0 \), \((x + 1)(x - 5) = (0 + 1)(0 - 5) = (1)(-5) = -5 < 0\).
   - For \( x > 5 \): Choose \( x = 6 \), \((x + 1)(x - 5) = (6 + 1)(6 - 5) = (7)(1) = 7 > 0\).

3. **Conclusion**: 
   The inequality \((x + 1)(x - 5) < 0\) holds in the interval \((-1, 5)\).

Thus, the solution is:

\[
-1 < x < 5
\]

### Answer:
The correct choice from the options is:
- \(-1 < x < 5\).

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Would you like further explanation on this problem or a related topic? Here are some follow-up questions you might find helpful:

1. How do we analyze inequalities with two factors like this one?
2. What is the significance of critical points in solving inequalities?
3. Can this inequality be solved graphically using a number line?
4. What happens if the inequality was \((x + 1)(x - 5) > 0\)?
5. How can this technique be extended to more complex polynomial inequalities?

**Tip**: Always check the intervals between the critical points when solving polynomial inequalities.

Jika (x + 1)(x - 5) < 0, x ∈ R, manakah x yang memenuhi persamaan tersebut?

Learn how to solve the inequality (x + 1)(x - 5) < 0 with a step-by-step solution. This problem involves critical points, interval testing, and the sign change analysis method. Suitable for students in Grades 8-10.

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