I would like to know the meaning of "so" in the next sentence.
The fire started at about 5 a.m., so he was sleeping.
It was 5am- a time at which it would be understood that people are typically asleep. It has nothing to do with the fire.
NOT A TEACHER
The meaning of so here is similar to that of therefore or consequently.
I think it is perfectly okay as written, especially if used as reported speech. The context around the statement would make it clearer I guess.