It sound to me as if your child is in danger of believing that her actions have no consequences. What you describe is, I believe, quite a serious episode of petulance. She threw things at you (including a plate of food) and hit you as hard as he could (it must have been hard for a five year old to "really hurt" an adult). She could have caused lasting damage or quite serious injury - particularly if the plate of food had hit you in the face. Despite being so young she is actually showing signs of serious anger management issues and it needs addressing.
If you look at my answer to this question:
https://www.theanswerbank.co.uk/News/Question1691261.html
You will see where I'm coming from. Of course I'm by no means suggesting that your child will take up knives. But my point in answering that question the way I did is to suggest that misbehaviour, unless addressed early on, simply persists and usually worsens.
I believe you should prevent her going to the birthday party. This was a serious episode of misbehaviour and warrants a serious sanction. She needs to learn that simply apologising afterwards is insufficient. Her bad behaviour has to stop ("..she apologises but then still behaves the same"). She seems to be developing the belief that her behaviour is perfectly acceptable providing she apologises afterwards.
Taers will no doubt flow and possibly even another tantrum. But how else wil she learn to moderate her behaviour? Your call, I think.