It would seem ridiculous to evict you for $3.39!
Maybe the owner is using it as an excuse:
I would first talk to other Tenants and find out is something is going on.
If they are still pursuing it, you should still have 30 days.
The Five-Day notice should have some contact info on it; City, County or Legal Aid; I would get more information before it is too late and you HAVE to move.
Maybe all you need is a little better communication.
Good luck and may God bless