To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.
The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:
[Insert image of two parabolas on a coordinate plane]
Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.
The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.