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 $(x-(-4){)}^2=4\ast 1\ast (y-6)$, 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 $4p=4\ast 1=4$. 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 $\boxed{{\displaystyle (x+4{)}^2=4(y-6)}}$, and the two points that define the latus rectum are $\boxed{{\displaystyle (-6,7)}}$ and $\boxed{{\displaystyle (-2,7)}}$.