A guest wants to rent my place long term (5 months) but has no reviews. I asked for references, she tried to send me the contact information for her current landlord, but AirBnB deletes all contact info from messages.
What can be done in this situation? Any way I can check her references without going outside of AirBnB ?
You can't. (There is a way to transfer the blocked information, but it is violation ot terms).
Accept the booking and then you have the options to check references. If not OK you can cancel the booking (with penalties). It's the risk of being a host. BTW If somebody provides the current landlord as a reference, it probably will be a positive reference.