I first misread your post (thinking your were on VA to SYD) and were obviously going to be looking for a hotel room near LAX.
The only thing I would prepare for is to know how to get from T6 to T5 if by bad luck you land out there. It is an airside tunnel walkway you would need to find.
Other than that, you are at the mercy of the Connection Gods.
EDIT: DL should give you a free change to an earlier BOS-LAX flight if you wish. If they refuse, HUACA.
EDIT2: Yes, paying for C+ would be smart.