Five years old is way too old to be having these kinds of tantrums. Has she always been violent when upset? Or is this a new behavior? You can definitely try professional help, but there are a couple of things you should try first:
1) If your child is still enraged after a time out, then you are not administering time-outs correctly. Time-outs should be one minute per age, so at five years, her time-outs should last five minutes. Time-out needs to be in the same place. It needs to be a small place, like a chair, stool, specific corner. If you just send her to her room, there are too many things for her to play with, break in a fit, etc.
The next time she hits, bites, kicks, or is violent in anyway, don't get upset. Use your best supernanny voice (not the accent, but calm and stern) and say, "That is inappropriate. Hitting is not okay and you need to go to time-out." If she won't walk by herself (which she probably won't at first), pick her up and carry her there. Do not say anything to her as you carry her to the time-out area. She might also hit or bite when you are carrying her, go ahead and ignore that. You're already taking her to time-out. The key is to not get upset yourself. At the end of the 5 minutes, while she is still in the chair/stool/corner, ask her, "Why were you sent to time-out?" IF she is still enraged, hits or gets violent, or refuses to answer or answers "Because you're mean", then say (in your calm supernanny voice), "This behavior is still inappropriate. You need to stay in time-out until you can act appropriately." This time, wait only two minutes, and ask her again, "Why were you sent to time-out?" Do not let her leave time-out until she is calm and can tell you what she did wrong. At that point, you can have a mini-discussion (remember, she's five, it should only last five minutes) about why hitting is wrong, what she can do to show her anger appropriately, she can apologize, and you make it clear that you are upset with her behavior but that you love her. It may take all day. I helped a friend through a similar situation one Saturday and it literally took three hours to get her son to calm down. But if you don't do the work now, it will get progressively worse and as she will continue to get bigger, one day she may actually cause you physical damage. You might want to ask a friend or family member to give you back up and remind you that you are doing the right thing. You need positive reinforcement as much as your child does.
The key things to remember are to (1) Stay calm, (2) BE FIRM- Do not give in because it's taking a long time or she appears to be getting more upset. She needs to stay in time-out until she is calm. PERIOD. END OF DISCUSSION., (3) Repetition and Consistency- use the same words "This is inappropriate" or something to that effect, go through the same exact steps to get out of time-out, do it every single time she gets violent, no excuses. I don't care how tired you are, how late it is, whatever. Again, if you don't stop this now, it will get worse.
2) If she really is polite and well-behaved for everyone else, you might want to talk to her teacher to ask for advice. You might also think about keeping a journal. Keep track of what she eats, how she sleeps, who she comes in contact with, and what her behavior is. Check for patterns. If she always throws a fit on days when she eats bananas, you might want to stop feeding her bananas. If she gets upset every day after she spends time with a particular child or neighbor, you should limit her exposure to that person. Basically see if there is anything in her environment that is setting her off and then change her environment.
3) If this is a new behavior, then you definitely need to take a look at what has changed that has caused this. Kids acting out can be a symptom of abuse. If there is a kid at school who is bullying her, she might be acting out at home because she can't defend herself against the bully. If there is a new adult in her life, I'd take a close look at that relationship. (I'm not saying your child is being abused. I'm just saying that radical change in behavior can be a sign and if this is new behavior, you need to figure out what is causing it.)
4) You might also want to talk to your child when she is calm about her aggressive behavior. Talk to her about why it's not okay to hit, what she should do when she is angry, how much it hurts you when she attacks you, etc. Maybe she needs to join a sport like soccer where she can channel some of her more aggressive tendencies in a positive way.
5) You might think about telling her that from now on, whenever she gets violent, not only will she go to time-out, but you will also take away one of her toys. Then do that. Don't use it as an idle threat. Go through with it. The next time she hits you, do the whole time-out thing and take away one of her toys. Keep it locked up where she can't get to it for at least a week.
Good Luck.