The equation given is $\frac{x^2}{4} - \frac{y^2}{25} = 1$. This represents a hyperbola centered at the origin with its transverse axis along the x-axis.

For this hyperbola:

• The transverse axis is horizontal because the $x^2$ term is positive.
• The vertices are at $(\pm 2, 0)$ since the distance along the x-axis from the center is determined by $\sqrt{4} = 2$.
• The co-vertices are at $(0, \pm 5)$ since the distance along the y-axis is determined by $\sqrt{25} = 5$.

The correct graph should reflect these features, specifically opening left and right. Therefore, the correct choice is D.