Is this enough to end a long term relationship?

Allie • Mom of 2
Okay so I have been with my boyfriend 5 yrs.  and have two kids together. Which is what makes this so hard. When we first got together we f***ed like bunnies multiple times a day all over the place (sorry if it's tmi) but then one day I found porn on his phone. I felt very hurt it's not like we weren't having sex and in many different ways. But I think the thing that hurt me the most was the girls in the porn he watches are like the complete opposite of me. We had a huge fight over it. But then we move past it and then I later find messages on his Facebook between him and another girl. I packed my bags and was gonna leave but then he deleted his Facebook and got rid of his phone so I thought maybe he is serious. So we fixed things and shortly after I got pregnant with my first daughter. And then I found the porn again. And again I was very hurt because we already had a fight over it and then the Facebook thing once again a huge fight but I did leave for a week to show I was serious and when I came back it seemed things had really changed and were really great. We shared everything knew each other's passwords. Had another child and things were still good. But now I found the porn again. And it seems like he only does what he needs to make me feel comfortable and then he slips again. It's very hurtful to me and I'm not okay with it and I feel if he was really committed to me he would gives this up. It's not like I'm asking him to completely change who he is as a person. 
I know people have their own feelings regarding porn and some women think it's okay. But I don't. I feel if you are in a committed monogamous relationship that means that one person only. 
So all that being said what's your opinion?? Should I leave if I feel so strongly about this? 
Or am I'm being irrational?? I don't what to tear my family apart he is a great dad but I can't help that guy punching heart crushing if feeling I get when I find it on his phone. tia

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