Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation.

Focus at $(-4,7)$; directrix the line $y=5$.

Step 1 ：Given that the focus is at \((-4,7)\) and the directrix is the line \(y=5\), we can find the vertex of the parabola.

Step 2 ：The vertex is the midpoint between the focus and the directrix. So, the y-coordinate of the vertex is the average of the y-coordinate of the focus and the y-coordinate of the directrix, which is \((7+5)/2 = 6\). The x-coordinate of the vertex is the same as the x-coordinate of the focus, which is -4. So, the vertex of the parabola is \((-4,6)\).

Step 3 ：The distance from the vertex to the focus or the vertex to the directrix is p. In this case, p is the difference between the y-coordinate of the focus and the y-coordinate of the vertex, which is \(7-6 = 1\).

Step 4 ：Substituting these values into the formula for a vertical parabola, we get \((x-(-4))^2 = 4*1*(y-6)\), which simplifies to \((x+4)^2 = 4(y-6)\).

Step 5 ：The latus rectum of a parabola is a line segment perpendicular to the axis of symmetry, passing through the focus, and its endpoints lie on the parabola. The length of the latus rectum is \(4p = 4*1 = 4\). Since the parabola is vertical, the latus rectum is horizontal. The midpoint of the latus rectum is the focus, so the endpoints of the latus rectum are \((-4-2,7)\) and \((-4+2,7)\), which are \((-6,7)\) and \((-2,7)\).

Step 6 ：So, the equation of the parabola is \(\boxed{(x+4)^2 = 4(y-6)}\), and the two points that define the latus rectum are \(\boxed{(-6,7)}\) and \(\boxed{(-2,7)}\).