Does she have a confirmed reservation? Is she asking to make changes to her confirmed reservation?
If both are yes, you could just reject the changes and tell her clearly and firmly that
1) the fifth person is not permitted and if brought in the entire reservation will be subject to cancellation on the spot for breaking house rules and fraud. (The fifth person will have to stay somewhere else.)
2) she cannot leave belongings there if she is not paying for nightly rental.
If you don't want her reservation with the gap in it at all then tell her she needs to either keep the reservation as is (since she would be paying for the space each night she could leave her things there while she is gone) OR she can cancel her reservation.
If you DO want the reservation with the gap in it you could say tell her that she would need to check out on the morning of the last day of the first part of the reservation and that since you are going in to clean and will have other occupants for the two weeks, nothing can be left there.
Or you could accept the fifth person for an extra fee. Decline or accept, up to you.
You can accept the proposal with the gap (essentially two different reservations) or not. Up to you.
If she doesn't want her original reservation she either needs to propose changes you will agree to accept or she has to cancel. She has no other choices.
If she is unreasonable and argues and refuses to comply with these simple rules, you can call Airbnb and ask them to find her another option, since she clearly doesn't want what you are willing to offer.
You might want to talk with her (you will have her number if she has a confirmed reservation) since messaging is sometimes not as nuanced and clear. Put all conversations in writing and send immediately so you have an Airbnb message thread to refer to.
If she doesn't have a confirmed reservation, just decline her inquiry or request. No penalty for declining "not a good fit" or "wants dates different than the requested dates" are your reasons.