hmmm..... job
#1 is to put the freewheel body back together (remove the inside half from the hub, put a little grease on the bearing races, put the bearings in the races, carefully mate the two halves, reinstall the cone and the shim washers).
As noted, the freewheel is designed to use threads on the small cogs and splines on the large cogs. You'll need to use two chain whips to unthread the small cogs in order to get to the large cogs.
I've got a photos of one of my SunTour Pro Compe 6 speed freewheels with "ultra" spacing. The Pro Compe has the same arrangement of splined and threaded cogs as the Perfect. The "ultra" spacing is a bit narrower than the 5 speed versions. This is achieved with a complex arrangement of spacers between the cogs.
Steve in Peoria
edit: the large cog on your freewheel doesn't look like something designed for a Perfect body. Is it off of a much later SunTour freewheel, maybe?