Karen. You certainly can paint that siding whatever color you like. VINYL siding can't be painted darker colors than original because it expands and contracts so much. VINYL siding painted a dark color can warp very badly.
So, now that you know you can do this. You need to pressure wash everything you are going to paint - remove all the chalk you can. Aluminum siding chalks very badly.
Once this is done - prime with an exterior alkyd primer - NOT Latex - you are not likely to get all of the chalk off - alkyd primers stick to residual chalk - latex won't.
After that - 2 coats of the best 100% Acrylic Latex paint you can find - sheen and color of your choice.