The focus at `(0,5)` the directrix `y=-5`.

Answer

To find the equation of the parabola with focus at (0, 5) and directrix y = -5, we will follow these steps:

### Step 1: Identify the Vertex
The vertex of the parabola is the midpoint between the focus and the directrix.

- Focus (F) = (0, 5)
- Directrix (D) = y = -5

To find the vertex (V), we calculate the midpoint of the focus and the directrix. The y-coordinate of the vertex is the average of the y-coordinates of the focus and the directrix.

\[ V_y = \frac{F_y + D_y}{2} = \frac{5 + (-5)}{2} = \frac{0}{2} = 0 \]

Since the x-coordinate of the focus is 0, the vertex (V) is at (0, 0).

### Step 2: Determine the Distance 'a'
The distance 'a' is the distance from the vertex to the focus (or from the vertex to the directrix).

\[ a = F_y - V_y = 5 - 0 = 5 \]

### Step 3: Write the Equation of the Parabola
Since the parabola opens upwards (the focus is above the directrix), we can use the standard form of the equation of a parabola that opens upwards:

\[ x^2 = 4ay \]

Substituting the value of 'a':

\[ x^2 = 4 \cdot 5 \cdot y \]

This simplifies to:

\[ x^2 = 20y \]

### Final Equation
Thus, the equation of the parabola is:

\[ \boxed{x^2 = 20y} \]

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