I have never had a therapist who I contacted on their cell. Maybe it's because I've always gone to community mental health centers and not private practices, but they just don't give out their cell numbers and they aren't a person to contact in a crisis. I personally really wouldn't feel comfortable taking my therapist away from her kids or her teaching or schooling or whatever it was she was doing at the time, whereas crisis and EMS services are there just to help in emergency situations like this.
If your therapist lets you down, I'm sure they have a crisis center or mobile crisis unit in your area, plus there are the suicide hotlines, in addition to 911, which you really need to be willing to call in the event that you make an attempt and change your mind and want help. There are also online and texting crisis chat services. My post count is not high enough to post links, but google "crisis chat." I've never used any of them, but they could probably contact your local police department for you if you needed it.
So I don't really know how it works with contacting therapists on their personal cell phones outside of office hours, but, like other people said, there have to be clear boundaries set up for that. I think a lot of people gave good advice here, but you came wanting to know if you should leave your therapist over this one issue, and I think that's something you should talk to him about. Just be honest and tell him that you're thinking of seeking a new therapist because of it and see if you two can work it out and solve the problem together. It would be a shame to end a 5-year therapy relationship, which presumably had been good or you wouldn't have stayed that long, over this one incident. But you also said that you might be too attached, and that's something that could take a long time to work through--but definitely needs to be brought up to him. Or your therapist might even think it's time to move on. My therapist and I have recently decided to part ways as I have been working with her for years and not really improving, so it's time to try someone new.