Explanation:

- The formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

- For points \((0, -5)\) and \((x, 0)\), the distance is 13 units:

$$ \sqrt{(x - 0)^2 + (0 + 5)^2} = 13 $$

- Simplifying, we have:

$$ \sqrt{x^2 + 25} = 13 $$

- Squaring both sides, we get:

$$ x^2 + 25 = 169 $$

- Subtracting 25 from both sides:

$$ x^2 = 144 $$

- Therefore, \( x = \pm 12 \). Since we're looking for a positive value, we choose:

$$ x = 12 $$

- Option 2, 12 units, is the correct answer