I'll try to answer the best I can but be aware that she, along with everything is still a WIP. And yes, 5 sentences is quite restrictive, but I believe this is what is known as an elevator pitch so I tried to compress the following so it would fit. Allow me to elaborate on what I have so far:
The theme surrounding her, and perhaps even the work itself, is the lack of love. Her parents are getting a divorce and she overhears them saying that neither wants custody of her. This leads her to realize that her parents never really wanted her as she always noticed a sort of distance between her and her parents. She wasn't getting the love she needs and tried to fill that void with others such as her friends and teachers. She thought that doing well in school would maker her parents love her but they just simply approve of her. If she does bad, then they get all authoritarian on her, so she tries really hard to do well in school. This has lead the approval from the school and decides to take charge of any situation, all just to get the love she desires. In reality, she just wants her parents to lover her like they should.
As for the reincarnation, she was born 10 years after her reincarnated mate and she's been having the same dreams of the medieval couple just like the ML. Unlike him, she does believe it is her destiny to be with him. Add to that the lack of love from her parents and she's pretty desperate to get with him, thinking he is what will fill that void.
Now we come to the part where I have not actually planned out so this is subject to change.
I think that if her parents loved her like they should, she would not have this strong desire to be loved and thus would probably assume the dreams were nothing more than that, like the ML. She'd probably meet up with him at the current time and be rational about the situation, as in, she'd probably wait till she grew up to be with him. But because that's not the situation, she's really desperate to have that void filled and her authoritative nature just gets in her way of rational thinking. But she is not without logic. She can, and will, come to terms that she can't be with him at the moment, but because she can't give up on him, will give him 4 challenges to prove his love for her, which will be the bulk of the story.
That's pretty much all I have for her at the moment. Again, she is a WIP as everything is currently in the planning stages.