Can't tell the brand from the photo, but given that it's an old 5 speed, old brands like Cyclo, regina, Everest and others come to mind. First of all is the freewheel working, as in freewheels backward, and drives forward? If so it's complete nad nothing is missing.
Look at the static part (turns with the hub, not the outer part with sprockets) of the freewheel for a raised or sunken ring with notches, or splines on the innermost clearance. That's what a removal tool needs to engage, and hopefully they'll be of a size and type for which removers are still available.
If you're still not sure, the brand and a well lit photo focused shot straight on, so the axle is out of the way and focused on the inner body may help us help you. BTW- back in this era, many freewheels needed to have the axle removed first in order to remove the freewheel.
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