What is #5 i don’t know the answer.

If the axis of symmetry is x=-1, the vertex will have x-coordinate -1.

The point (0, 5) cannot be the vertex. The friend is not correct.

If the point (1, 5) is on the graph so is the image of that point when it is reflected across the axis of symmetry. That image point is (-3, 5). A parabola that goes through points (1, 5) and (-3, 5) will not go through point (0, 5).