What facts should I give him ?

I've been dating for 5 years and the last 2 years, I've always been finding flirtatious and sexual texts in my boyfriend's phone, but I ignored it and let it slide. About a week ago, he went through my phone and found a some deep flirting in my phone and we had a big fight, it got a bit physical and he left and we broke up and I knew we were done and we would never get back together again. He had left his phone at my place so i went through it and found out he had cheated on me twice this year and thrice last year. In grief, on the same day, I called a close friend and he came and comforted me, we got drunk and partially had sex, since I was high, we stopped. In the morning, my boyfriend came and found me with this guy and found condoms. But we talked about it and agreed we would try our relationship again. In the evening, he said he can't do it unless I have facts as to how the relationship will work. I know I messed up getting with another guy less than 24 hours and I have no excuse for it. But even after everything, I still want to be with this guy and I know it won't be easy but I know it can work. What facts can I give him to allow us to try again ? How do I go about this ?

[I've been dating for 5 years and the last 2 years, I've always been finding flirtatious and sexual texts in my boyfriend's phone.] You've been dating for 5 years (still no marriage?? :-O (A)) this is why you found flirtatious and sexual texts in your boyfriend's phone. [I know I messed up getting with another guy less than 24 hours.] You've both messed up in this relationship. Better to move on,where there is more trust in the relationship.