Totally sounds like you have a child with sensory issues. My daughter was like that. Except she wasn't so obnoxious, and she did not run the family. We started taking her to see a Childhood Specialist when she was 5 years old, so she could learn how to self-regulate herself and I as a parent could learn how to deal with her and relay what the Specialist told me to my husband, so we could work together on our parenting.
When she was 7 years old, we switched the entire family over to eating organic and using reverse-osmosis water as well as eliminating gluten, cow dairy/casein, and soy from our diet (that included doing away with almost all fast food and eating out; we only have 4-5 restaurants we will even contemplate eating at, and that's because we are able to get food there we're able to eat/that's in the realm of what we want to put in our body).
It was like night and day, the change was so dramatic.
She is now 14 years old, has a whole bunch of friends, she plays tenor sax in the band, plays goalie for Lacrosse, and is on the Highest Honor Roll. She rarely ever has a meltdown, we have had the best of times (so far) in entering the teenage years, and as of Thanksgiving 2013, we have evolved our diet even further and are now doing Paleo. She and I go to a spiritualist church, and we do a lot of different types of alternative medicine (chiropractic and acupuncture are the favorites). She still has her quirks, but her mind is so much more settled now. Being on the Paleo diet, she's even starting to shed some of the weight she just couldn't seem to get rid of (she has hypotonia, so slow moving is like her middle name).
I would definitely look into doing a very big change in diet. Take out processed and preserved food (stuff bought from the store; your own canning and freezing is fine), SUGAR of all kinds (the only ones I would give her would be low-glycemic: pure maple syrup, raw honey, coconut sugar (but very little), dates and figs (watch now much is used; very sweet, can become high glycemic very quickly), pureed fruit like applesauce, and Stevia (I'm adding these because these are safe to cook/bake with. If you're going to get rid of the bad stuff, you'll need to do your own cooking and baking), DEFINITELY get rid of any and all artificial sweeteners, prepackaged food, fast food, junk food, candy, etc,. and replace with organic veges and fruits and (organic) free-range meats and eggs. Nuts, seeds.
I would even go a step further and suggest getting rid of all grains in the diet, simply because grains are very inflammatory, and through my own personal experience with helping my own daughter, sensory issues are because the brain is highly inflamed. Taking out everything from the diet that has any potential for causing the brain to inflame will help in quieting all of these quirky things your daughter is doing. Believe me; I have read hundreds of books on all different topics in my pursuit of helping my daughter. In fact, I have even gone back to school to become a health and wellness coach, so that I can help other parents help their children (and also for parents themselves to take back control of their health).
Your daughter will probably absolutely hate you and fight; I would wager that the foods she is eating are what is triggering the vast majority of her problems in that all of the synthetic, man-made stuff in them is probably an allergen for her body. Stand firm; offer her what food(s) she is allowed to eat. When she is hungry, she will eat. She is 5; she can't drive to the store and get food for herself. You as the mom have the ability to help her change her eating habits and to help her. My suggestion is to change what the whole family eats; the new diet/way of eating will help your daughter as well as everyone else.
I think if you take out all the bad food (and along with it the artificial dyes, the artificial flavors, the artificial sweeteners, the chemicals and preservatives, the MSG/excitotoxins, etc.) that you'll begin to notice quite a difference in your daughter within even just a matter of days.