Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. f(0, –5); y = 5

Well, "the set of all points in the plane equidistant from the focus and a line", is referring to the focus point of the parabola and the directrix line.

bearing in mind that, both fellows are at a distance "p" from the vertex, that puts the vertex right in the middle of them.

notice, the focus point is below the directrix, meaning, is a vertical parabola, and is also opening downwards, like in the picture below.

from -5 to 5 over the y-axis, there are 10 units, so the "p" distance is 5, so that puts the vertex right at the origin.

since the parabola is opening downwards, "p" is negative, thus -5.