Solution

38290

First name
Sam
School
Bridgewter High School
Country
Age
14

She can raise her balance by £5 by depositing (or cancelling if the number is negative) the following number of transactions:

For any given integer n:
3n+1 lots of £2
1-2n lots of £3

2(3n+1)+3(1-2n)=6n+2+3-6n=5