Does "Could you change a £5 note for me?" mean "exchange a £5 note for the same amount in different coins"?
But How about I have some coins totaled £5 and ask for exchanging them for a £5 note?
... although in real life (rather than an exam) you'd just present a handful of coins (worth $5) and say 'Have you got a five?'. In the UK it's the same, but with £5 and 'fiver'. Of course it might be appropriate to make the request more polite ('Could you give me...?') but it would still be excessive to give full details of the exchange.