Search Results: how can i prove to him i love him still

So, I have been with my girlfriend for a long time. About 5 1/2 years.

Early in the relationship (around the 3 month mark) she lied to me about her ex texting her. It happened while I think I was looking at her phone whike she wrote a note. I didn't see what it said. She lied and said it was her female roommate that texted her (Completely different names). I gave her about a dozen chances to tell the truth. Finally I told her I already knew and saw. She admitted she got a text from him, but it that she isn't doing anything, he just tries to text her sometimes, and since I had a friend/family member dying of Cancer at the time (R. I. P. Joe Basara), she didn't want me to worry and overthink.

There have been a few more small lies, omissions of truth, and more over the years, but I legitimately believe she loves me. We have been with each other through some of our more difficult times thus far, and she's a very emotionally feeling person. She loves animals, she can't handle people or animals being hurt without bursting into tears, etc.

But I still don't trust her completely. I haven't trusted her since that day when she proved she could lie right to my face. We have been long distance for about 3 years (Her family moved and we weren't equipped to move in together at the time), so I wouldn't even know if anything was going on.

She also lied about the state of her coworker's marriage. She claims she didn't know, but they were in a really bad place and about to divorce. She showed me her texts to make me feel better, and while he definitely talked about the marriage being in a bad spot, there didn't seem to be signs of anything more than him mentioning it and just being an acquaintance. Messages likely weren't deleted.

How can I trust her again? Should I?