Transport between 2 airports in early morning 5~7am?

Hello. I’ll be arriving at Pudong airport at 5:30am and my connecting flight departs from Hongqiao airport at 9:30am on the same day. Is there a bus or train in this early morning?
Night bus ends at 5am and the daytime bus starts at 7am? Should I just wait for the first daytime bus at 7am and will it be safe? Or is there any other way?
Both flights are international, from Europe to Pudong, and from Hongqiao to another Asian country, if that matters.
Thank you in advance.