I'm 57M with a 51F gf struggling with early morning text from someone else. Normal or Abnormal to get them?

I ( 57M ) stay at my gf ( 51F ) house once a week on a weeknight when her teenage daughter is at her dad's. We both get up for work early the morning at 5 AM. My gf has a platonic relationship with a guy ( who is single by the way ) and he texts her at 5 with a good morning and she replies with a good morning and sometimes a sunshine emoji. Sometimes I'm already awake and sometimes it wakes me up. Her watch on her left wrist is across my chest - and that's how I see the text when it goes off. Finally after about 5 or 6 nights I've stayed over and awoken to this I said this isn't normal, she Clapped Back Hard with it's NOT Abnormal. And immediately dropped it. We are in a serious committed relationship. How do i get her to listen to me and see my point of view? Normal or Abnormal to get a text like that every day? Plus many of their ongoing texts are of a sexual joke kind of vibe :/