What you said
You should be getting support from your head and deputy, not just being told to "reward good behaviour". In this situation, my head would have frog-marched said five-year-old out of the classroom.
Carrots are nice and should not be forgotten, but sticks are a greater incentive. Admonish her, and if she continues after this warning punish her in steps: five-minute break; 10-minute break; naughty seat; phone call; isolation. Every. Single. Time.
The expert view
I don't blame you for wanting to do everything you can for this child - it marks you out as having the DNA of teaching excellence, as you possess at least one of the credentials of the professional educator: you care about the child's well-being. But that compassion must not be allowed to overrule practicalities. This child has rights, but is now destroying your mental well-being and the educational space of your class. That cannot be right.
The approach recommended to you by the school is well-meaning, but wrong. You have been advised to tame this child with love, which is sweet, but not all problems can be solved with compassion alone. You have been urged to try to motivate and persuade, but this child does not want or care for such persuasion. She needs to be shown boundaries, so use sanctions.
Every time she gets out of control, you (or the teaching assistant) need to take her out of the room. This will minimise the impact on the others. The pupil could be taken to another class, to the head, or to a quiet space with the teaching assistant.
You should also pursue any sanctions available, such as detentions, or calls home.
Tom Bennett is author of `The Behaviour Guru' and `Not Quite a Teacher': http:behaviourguru.blogspot.com
Post your questions on: www.tes.co.ukbehaviour.