ProPresenter handles the shadow (or drop shadow) of text and objects from the Object Properties tab. Shadow is not considered a text property, so you won't find it on the Text Properties tab in the Editor. The screenshot below is from ProPresenter 6, but is the same setting and location in previous versions as well.
With your text box selected, go to the Object Properties (fourth tab on the right) and enable Shadow. You can set the color, angel, length, and radius (blur) of the shadow. If you are applying a shadow to any other object on the slide, the process is the same. Select the object then set your shadow properties.
If you add a Fill Color to the text box, the shadow moves behind the entire box rather than being behind the text. If you want text to have a shadow and you want a colored box behind it, add a separate shape object and place your text box over it.