There's something going on here, and it's your job to figure it out. :-/ That's usually best done by talking once the child is calm. But there are a lot of things you can try to improve the immediate situation.
Hitting, kicking and screaming are not "OK" behaviors in response to anger. Neither is your distress. This is just a behavior, like thumb sucking or crying when a child doesn't get what they want. Try to remember that, even if the words are extreme and painful.
Anger is not usually a primary emotion (some will argue that point.) Usually it's a secondary emotion; it gives the person an outlet which feels more effective than identifying the underlying hurt (or the primary emotion) and talking about it. But talking about things is what's necessary to get your child to understand her emotions and to control them.
The first step in talking effectively with your child is to give her a rich emotional vocabulary1 that she really understands. A 5 year old can understand frustrated, unimportant, ignored, unloved, lonely, overwhelmed, etc. (There are lots of positive feeling words as well.) Naming a feeling is necessary to deal with a feeling.
When a child is misbehaving, my way of dealing with it was to remind them of what behaviors are and are not acceptable (these have to be discussed ahead of time, as do the consequences.) If the child received a warning about the behavior and they did not exert self control (the ultimate goal), they got a time out. (My favorite book on time outs was 1-2-3 Magic by Thomas Phalen. One of the things I loved about it was that arguing is dispensed with entirely; a parent can remain quite detached from the child's behavior. The counting also gave the child a chance to reconsider their behavior. If they stopped before reaching three, they got a sticker, which was redeemable for something desirable (the more involved, the more stickers needed. But have things they could earn with just a few stickers, too. Small Lego sets were an option for us.)
Time outs began when the child was quiet (wherever, e.g. in their room), i.e. if they are kicking and screaming, their time out didn't start yet. Just a reminder that their time out hasn't started yet is all the involvement you need to have (I would let her kick and scream. If she damages something, I would have her help repair it at a later time.) When they've quieted down, start the timer and let them know. That's it; no arguing, no "punishments", no drama. After the time out, or as soon as convenient, you have a discussion about the child's feelings. Let them know their feelings are very important to you, and let them find security in your unconditional love (which does not mean you tolerate bad behavior. Discuss alternate ways they can deal with their feelings. Do some role playing.
This might just be a phase, or something could be triggering it. You need to look for patterns which might suggest what the problem is and how to best deal with it. But talk, and remain open to what your daughter has to say.
Sorry this is so long. :-/
1 These lists - and activities to reinforce them - are easy to find on the Internet.