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The question provided is asking for the following:

**Given:**
- \( x = 5 \) is a solution for the quadratic equation \( 5 + mx - 2x^2 = 0 \).

**Task:**
- Find the value of \( m \) and another value of \( x \).

### Step-by-Step Solution:

1. **Substitute \( x = 5 \) into the equation:**
   \[
   5 + m(5) - 2(5^2) = 0
   \]
   Simplify the equation:
   \[
   5 + 5m - 2(25) = 0
   \]
   \[
   5 + 5m - 50 = 0
   \]
   \[
   5m - 45 = 0
   \]
   \[
   5m = 45
   \]
   \[
   m = \frac{45}{5} = 9
   \]

   So, \( m = 9 \).

2. **Find another value of \( x \):**
   Now, substitute \( m = 9 \) back into the quadratic equation:
   \[
   5 + 9x - 2x^2 = 0
   \]
   Rearrange the equation to standard quadratic form:
   \[
   -2x^2 + 9x + 5 = 0
   \]
   Multiply the whole equation by \(-1\) to make it easier:
   \[
   2x^2 - 9x - 5 = 0
   \]

   Now, solve for \( x \) using the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \( a = 2 \), \( b = -9 \), and \( c = -5 \).

   First, calculate the discriminant:
   \[
   b^2 - 4ac = (-9)^2 - 4(2)(-5) = 81 + 40 = 121
   \]

   Now, solve for \( x \):
   \[
   x = \frac{-(-9) \pm \sqrt{121}}{2(2)} = \frac{9 \pm 11}{4}
   \]
   So the two solutions for \( x \) are:
   \[
   x = \frac{9 + 11}{4} = \frac{20}{4} = 5
   \]
   \[
   x = \frac{9 - 11}{4} = \frac{-2}{4} = -\frac{1}{2}
   \]

   Therefore, the other value of \( x \) is \( x = -\frac{1}{2} \).

### Final Answer:
- \( m = 9 \)
- The other value of \( x \) is \( x = -\frac{1}{2} \).

---

Would you like further details on any step? 

Here are five follow-up questions to help you explore this further:
1. How is the quadratic formula derived?
2. What are the conditions for a quadratic equation to have real solutions?
3. Can you show how to factorize the quadratic equation \( 2x^2 - 9x - 5 = 0 \)?
4. What happens if the discriminant is negative?
5. How can we check if the solutions for \( x \) are correct?

**Tip:** Always double-check your solutions by substituting them back into the original equation to verify their correctness.

Jika x = 5 ialah suatu penyelesaian bagi persamaan Kuadratik 5 + mx - 2x^2 = 0, cari nilai m dan satu lagi nilai x.

Learn how to solve the quadratic equation 5 + mx - 2x^2 = 0 when x = 5. This solution includes finding the value of m and using the quadratic formula to solve for another value of x. Suitable for students in Grades 9-10.

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