Difficult to answer your question because each admission authority that operates a review process has its own way of doing things. For example, there's at least one authority (not yours) that will not take into account extenuating circumstances at all!
As far as I'm aware, N. Yorks will
consider any relevant evidence. What I can't be sure about is whether going for a review would then limit your rights at an independent appeal, so you do need to establish what their policy is.http://www.elevenplusexams.co.uk/11plus ... rs.php#b18
I could give you my own view of the academic evidence, but would need to know much more. Is there any indication of the sort of level 5 the school is expecting for Maths (5a, 5b, or 5c) and for teacher assessed Science? And what about English?
Have there been any optional SATs tests? What about academic evidence prior to year 5 - for example, what results were achieved at KS1? Looking at school reports in years 3-4, is there any mention of high achievement?
Does the school have the results of any CATs or NFER reasoning tests?
Has the school setted for maths or English at any point in time, and if so, which set was your daughter in?
It's good that the head is being supportive, but I would have thought the school would need to provide as much academic evidence as possible.