I don't care if anyone texts me at 5am. Bizarrely, I don't have my mobile phone in my bedroom at night. 
Ergo, I don't get disturbed by the text!
Have to wonder why someone would text at 5am though! Aren't most people asleep then? If I am ever up in the (very) early a.m, I wouldn't dream of sending a text to anyone.
Although, as I said, it doesn't bother me if people send them to me, as I leave my phone in my bag in the kitchen. I think I have only received a text in the small hours a couple of time though.
Most people do have the decency and common sense to text people in normal daytime hours
Have to ask, why do people take their mobile phone into their bedroom? 
You don't need it at night. Before mobile phones existed 15-18 years ago, you never had a phone by your side in the bedroom (and I am not going to believe everyone has/had a phone in their bedroom!)