What should I do if my girlfriend isn't completely over her ex?

Okay, well my girlfriend and I been dating for almost 5 months. I know it seems like we kinda took it fast, but we’re very much in love with each other. Its getting the point where we are getting serious about us. The problem is, she recently admitted to me that she isn’t completely over her ex. Her and her ex been together for 5 years and they broke up last year. When we first started talking, she said she’s over him and she doesn’t love him. Now she said she still loves him (not in love with him), misses him, and cares about him. She clearly said she doesn’t want to be with him regardless because it will be like before and she will always be hurt. She said she wants to be with me. She even said that she may not be 100% faithful with me if she hangs out with her ex. This is where I feel skeptical about her. I know it takes time for her to move on and completely get over her ex, but what should I do? I feel uncomfortable when she said that she still loves him, misses him, cares about him, and the fact that she may not be 100% faithful with me if she hangs out with him. I feel like I can’t trust her as much and I have doubts about our relationship. I really do love her and I don’t want to lose her, but I am not going to get played like my past. So you guys tell me what you think I should do and why. Thanks, I appreciated it very much!