I'd say just do what most of the pop-science books do. Just mention that spacetime has four-dimensions and is curved, without really going into what this curvature means. Perhaps mention what it curvature really means is too complicated.

Alternatively if you decide to keep the idea that spacetime is curved "in" something else, you could say that spacetime is four-dimensional, but is curved in six dimensions. Spacetime's curvature is actually to drastic to fit into five dimensions but does fit into six. That'd only involve a small change in your slides.