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I might be a laymen, and I have nothing to back my ideas up, but...

I don't agree with the idea that gravity or matter would be diminished in 5D or 7D worlds. If anything, I think that as you go to higher dimensions, its always a case of 1 step backwards 3 steps forward as far was what you can perceive there. In other words, eveything shrinks down a little in size because that dimension is technically existing at a higher "resolution" but there is so much more detail and information in that dimension, that you actually perceive the items to be bigger and much more detailed. Smoothe surfaces by 3D standards are probably rougher and uneven in higher Dimensions.. However if you were to make something smoothe in a higher dimension and then perceive it at 3D it would probably seem impossibly smoothe to the point where its details almost might seem indistint or washed out. And chances are, you'd always have the feeling that you should be seeing more to the surface, but it would be beyond your perception. You can see it, but it be hard to look at long, because you'd feel like you are looking at it with crossed eyes or as if you were looking at something your eyes couldn't quite focus on..

The same thing applies to gravity. Technically I think gravity is a solid force that exists equally throughout all of the dimensions, but I think that if you were a 3D person visiting people in a 5D world, they wouldn't feel the gravity any heavier than you feel our Earth's gravity, but to you it would seem much heavier, because you would actually be getting more detail and information of the force of the pull.. Whats more, you might even be able to tangibly feel pressure points from the gravity, and maybe even see it to an extent.. This is all of course, assuming that going more than one dimension up doesn't result in enough information that the gravity just crushes you on contact. Keep in mind that if you double both sides of the resolution of a monitor you have quadrupled the total amount of information on the screen. Each dimension might follow similar laws. And since we think of the dimensions as branes now, I can't help but think of it as a giant LCD screen with a slightly prickly surface..