The given equation of a parabola has a focus at \((-5, 0)\) and a directrix of \(x = 5\). The general form of the equation for a parabola with a horizontal axis of symmetry is:

\[
(x - h)^2 = 4p(y - k)
\]

where \((h, k)\) is the vertex of the parabola, and \(p\) is the distance from the vertex to the focus or the directrix. The focus is \((-5, 0)\), and the directrix is \(x = 5\).

### Step 1: Find the vertex
The vertex is midway between the focus and the directrix. The focus is at \((-5, 0)\), and the directrix is a vertical line \(x = 5\). The distance between the focus and the directrix is:

\[
\text{Distance} = 5 - (-5) = 10
\]

The vertex is halfway between them, so:

\[
\text{Vertex} = \left(\frac{-5 + 5}{2}, 0\right) = (0, 0)
\]

### Step 2: Determine the value of \(p\)
The value of \(p\) is the distance from the vertex to the focus. Since the vertex is at \((0, 0)\) and the focus is at \((-5, 0)\), we have:

\[
p = -5
\]

(The negative sign indicates that the parabola opens to the left.)

### Step 3: Write the equation of the parabola
Now that we know the vertex is at \((0, 0)\) and \(p = -5\), the equation of the parabola is:

\[
(y - 0)^2 = 4(-5)(x - 0)
\]

Simplifying:

\[
y^2 = -20x
\]

This is the equation of the parabola.

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Do you want further details or have any other questions?

### Related Questions:
1. What is the equation of a parabola if the focus is shifted to a different point?
2. How do you find the directrix of a parabola when given its vertex and equation?
3. What happens if the directrix is horizontal instead of vertical?
4. How does the value of \(p\) affect the shape and orientation of the parabola?
5. Can you derive the equation of a parabola when both the focus and directrix are tilted?

**Tip:** The vertex is always halfway between the focus and the directrix.

Learn how to find the equation of a parabola with a focus at (-5, 0) and a directrix at x=5. This detailed solution covers key concepts in conic sections and coordinate geometry, perfect for students in Grades 9-10.

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