Sounds like the child is lead by her emotion. Some people are more emotional then others. The question is where is her safe zone (quite area). This is where she can go to, to calm herself down. She can slowly get to a point where she can get the things she needs and go to that area. That way she could get the emotional need and learn how to handle her own emotion.
Specialmom is exactly right. There is a set of books that you may find helpful as they are aimed at this age group. "Cool down and work through anger" or "When I feel angry". This is part of a series of books aimed at 4 to 7 year olds and meant to be read to them at night (several times) and then practiced. Kids do need to be taught how to deal with anger. You do not try and use these techniques while she is screaming. But once she stops or later on in the day - you can refer back to them or pull the books back out.
You can find them here - http://www.amazon.com/Cool-Through-Anger-Learning-Along/dp/1575423464/ref=pd_sim_b_5
If you go to the site mentioned above you will also find other books aimed at various situations that kids might find themselves in - if anger is not quite what you are looking at.
Hello! Now why would anyone be judgmental about your post? :>) This can't be super uncommon and we ALL have things we have to work on with our kids. Honey, if you saw my list . . . whew. ha ha. Anyway, the thing about 5 is that they haven't learned the proper way of expressing emotions. You are such a smart mom to start working on it because kids really CAN become adults that haven't learned proper coping skills and they react, pout, etc. I'm sure you know one or two like this. So, teaching our kids how to handle difficult situations is important.
Couple of things you can do. First, have conversation about the RIGHT way to handle frustration, hurt or anger. What can you do, what can't you do. Even go as far as to act it out for her. stress no tears, no upset voices, etc. and that deep breathing, going to a clam down corner, giving herself a hug (as deep pressure/hugs is soothing/calming).
However, I guess I should ask what exactly you want help with. Maybe it isn't her behavior but how she can be less sensitive. If you could clarify that, I'll help in a different way if I can.
Anyway, another important thing to do is to make her feel the emotions at home and in a safe place. Take something from her as a child does. Win a game that she thinks she is about to win as if she is playing with a playmate. And then as she reacts, help her with handling it appropriately using the strategies you talked about with her (hugging herself, going to a clam down corner, pushing a wall -- we call it a push over but again, that pushing sensation is soothing to the nervous system), take deep breaths, etc.
We have to guide our kids through appropriate reactions to things to help them learn. It doesn't come naturally for everyone. good luck