Final answer:
The axis of symmetry for a parabola with a vertex at (-5, 10) is the vertical line represented by the equation x = -5.
Step-by-step explanation:
The axis of symmetry for a parabola is a vertical line that passes through its vertex. Given that the vertex of the parabola is at (-5, 10), the equation for the axis of symmetry can be represented as x = -5. This is because the axis of symmetry will have the same x-coordinate as that of the vertex. For any parabola, the axis of symmetry is always x = h, where (h, k) are the coordinates of the vertex.