I have 5 kids, 9- and 10-year-old-boys, a 5-year-old girl, a 3-year-old boy, and a 17-month-old girl. My 5-year-old is having the exact same issues with both of the younger children. I actually remove her from the group when she is not being nice. I have her go play in her room by herself, and she cannot come back until she will apologize. She is then required to "mend the relationship" by playing nicely with whichever sibling she hurt or teased for 10 minutes before she is allowed to go about her business.
She does not always do this willingly and sometimes is sent back upstairs. She has had temper-tantrums and recked her room a few times, but she is required to clean it up, or the toys that she refuses to pick up get thrown out or donated (you only have to do that once or twice- the price of the toy does not matter as much as your daughter's respect--guaranteed your daughter will acquire more stuff, you should see my house with 5 kids worth of toys). All of this is done very matter-of-factly. If A, then B and B always has to happen --it cannot be a threat. There is no anger or frustration in any of this.
The acting out with my daughter is a want for attention. Being removed from the group does not feed into the whole attention thing. All of my children require and receive their individual 1-on-1 time. It does not have to be hours and hours. My 5-year-old loves to help me cook, so when I'm making dinner, she rips up the lettuce for a salad and is happy. My husband or I read to her at bedtime every day
1-on-1 too.
Whatever you decide to do, make sure all the adults in her life are on the same page and reacting similiarly, or she will get confused and play you against each other to get the attention she wants. Most kids try this and how successful they are at it usually mirrors how often you see the behavior.
Good Luck!