What do I tell my ex girlfriend?

So after 5 months were talking again. It seems as though she has feelings for me, because I remember after we'd break up in the past she would act this way, and we would always end up back together. Well we have been progressing, but now she is asking if I did anything with other girls while we weren't talking. I told her what I have done is none of her business, and what she has done is none of mine, and this best thing is to let it go, but she said she has to know or we can no longer speak. I liked the direction we were going in, but it has come to a halt because I won't answer her question. Has anybody been in this situation before that could help? Please help me. I told her I don;t want to know what she's done, but if I tell her then I would have to know just for some sense of balance and fairness. I think its best that we just drop it so no one gets hurt, but she doesn't want to do it that way. She says it won't bother her, but I'm pretty sure she's only saying that to get an answer out of me. So, any suggestions as to how I should handle this?