Four breakups.
You dating another. "MY G/F of 5months(we are in a' kind of' relationship)..."
She hurt, accusing.
You annoyed, stressed.
For what it's worth, if you can work 4 breakups into a 5-month relationship then it never was officially ended, just consuming itself. And even if she was wrong to take you for granted that Saturday, imho going out with another woman was payback.
Personally, I would have been deeply hurt.
More importantly, the level of drama sounds toxic and hurtful to you both...I'm not sure what you'd gain by having an adjudication on who was "right" or "wrong" that Saturday. I have no answer on that.
My question, if you also tend to retreat and stop speaking to your gf for long stretches, is: are you sure you're ready for an intimate relationship? In honesty, it does not sound like it to me. Maybe there are undealt-with issues from your early years, likely about your mother, that are being played out now?
IOW, the definitions of things (kind of in "a relationship", whose behavior was "worst") -- don't matter as much as the feel of things. And the consequences of things.
Have you ever considered getting some advice from a wise therapist about why your relationship is so tumultuous? I'm sure part of the reason is within the woman. You can't do much about that. But what about the part that's within you...want to tackle it?
I am guessing that you're relatively young. (Forgive me if I'm wrong.) If so, I can say that you would be so so very glad in future years if you dig into these issues and try to get help sorting them out now, rather than when you're in your 40s or 50s and broken hearted from divorce/s.
Hopalong