The general form of the equation for an ellipse with center (0,0) and semi-axes lengths a and b is:
(x^2/a^2) + (y^2/b^2) = 1
Since the vertex is at (5,0), we know that a = 5. Since the co-vertex is at (2,0), we know that b = 2.
Plugging these values into the equation, we get:
(x^2/5^2) + (y^2/2^2) = 1
Simplifying, we get:
x^2/25 + y^2/4 = 1
Therefore, the equation of the ellipse with center (0,0), a vertex at (5,0), and a co-vertex at (2,0) is x^2/25 + y^2/4 = 1.