[amptramp]

C5, the capacitor with the coil wrapped around it and connected in series with it is a chassis ground to AC line bypass.  They used a large value capacitor here which typically would have a lot of reactance.  The series coil is designed to resonate with the capacitor to bring the impedance down at frequencies of interest (usually the IF frequency).  Later in the history of the All-American Five design, the standard AC-DC five-tube radio, engineers went to 0.05 µF with no series coil.  If you replace it, it is your choice whether you retain the coil and it would probably be unnecessary but it would be cool to restuff it and retain the coil.

I have a box of yellow film caps here from justradios.com that I bought from Dave Cantelon directly at a London Vintage Radio Club meeting in London, Ontario and none of them have failed or drifted, so those are my choice for any recap job.