Ticket #1 LAX-PVG-LAX, Ticket #2 PVG-TPE-PVG

Is the 72 hours free transit apply or do I need proper visa?
Ticket #1 LAX-PVG-LAX depart LAX arrives PVG 5pm on day 1,
Stay in Shanghai 1 day <<<--- 72-hours policy ok?
Ticket #2 PVG-Taiwan-PVG departs PVG 2pm.
Stay in Taiwan 4 days,
Ticket #2 PVG-Taiwan-PVG, departs Taiwan arrived PVG 5PM on day 5,
Stay in Shanghai 2 days <<<--- 72-hours policy ok?
Ticket #1 LAX-PVG-LAX, departs PVG arrives LAX.

Since Ticket #1 duration is more than 72-hours in Shanghai... Will I need a proper entry permit?