I believe it is sleep paralysis - but a perfect starting point for a lucid dream. A LD I had a while back involved the same sort of progression as you described, but instead of floating I was sinking, and I could feel the "barrier of reality" like the division between water and air. Rapid heartbeat is just excitement, and the anxiety could be related to the unfamiliarity of the feeling. The rapid heartbeat can wake you up, too. It's important to concentrate on relaxing every muscle, including the heart, in your physical body.

As to getting to sleep in 5 minutes? The less you think, the better. But you can't think about not thinking. I can get sleep times down to within 10 minutes by concentrating on a single simple virtual object, like a piece of string, and not not thinking about not thinking about anything else.