Beginning a text chat with "Hello, I have a few questions about xyz and was wondering if now would be a good time to talk?" is considerate of the other party's time and attention, and it does not cost you anything but seconds to provide this context up front.
Edit: you edited and lengthened your comment.
> The protocol is then something like: "me-to-person-a: hello". wait for 5 minutes. no respone. "me-to-person-b: hello". wait for 5 minutes. no response. "me-to-person-c: hello"
I'm sorry, this is _insane_! That's 10 minutes to send out 3 words of communication, and the people who don't get back to you right away will now be getting back to you later to clarify, further worsening your signal to noise ratio! You could have spent 20 _seconds_ composing the first message with a one sentence synopsis. "Don't worry, no one is dead" or "The factory is on fire" are useful to know up front. You could copy and paste it to the next two people if they don't get back to you.