There are only 4 dimensions, 3 for space, and 1 for time. All other is junk science founded upon too many bad theories piled upon what-ifs, using mind-numbingly bad examples.
Well, yes and no. There are many mind games involving multiple spatial dimensions. Even multiple timelines at once.
We can see, feel and apprehend 3+1 dimensions. But that's no proof that there could be more dimensions of which we aren't aware of.
An attempt to approach the problem (with my insufficient english):
Imagine an ant running through your garden. From the perspective of the ant, everything looks giant. Single blades of grass seem to be high sequoia trees. And single grains of sand are like mighty rocks. Suddenly, the ant has to stop because a massive and glossy wall rises high into the sky.
If we now change the scope from the "microscopic view" of the ant to our "normal view", we will see that the massive glossy wall is just the hosepipe lying in the grass. Change the view again and imagine looking out from a high place, like from a high tree or maybe an airplane (well, this could be too high...): the hosepipe, a 3-dimensional object, "shrinks" to a 2-dimensional line, lying on the ground. And from a satellite's view, the 3-dimensional hosepipe is lying on the surface of a giant sphere - the earth. (Remember: centuries ago people thought that the earth is flat instead of a sphere!)
From this point of view, we can't see the 3-dimensional nature if the hosepipe anymore. We still know that the hosepipe is a 3-dimensional object. Imagine someone who always lived on an airplane with no connection to the ground. And he always wanted to know more about those funny lines lying on some green something...
That's the situation we are in now. Well, part of it. There are maybe some more dimensions, wrapped around our 3+1 "everyday life dimensions", but we can't be aware of them, because we're the giants.
I suggest reading of "Diaspora" by Greg Egan. It's an awesome science fiction novel with a plot set into multidimensional universes. Highly entertaining Hard SF.