I'm a US citizen visiting Manila. I want to visit Shanghai for 4-5days coming from Manila and back

Joji, you need it and you should apply for it in advance if you travel like that because you will fly back to Manila after visiting Shanghai, but in principle, you should go to a third country or region if you want to use the 144 hour free transit there.
Actually, if you travel like Manila-Shanghai-HK-Manila, you will be eligible for the 144 hour free transit in Shanghai.