A freewheel has the teeth screwed onto the freewheel body. You can remove the freewheel and sprockets. A free hub has the freewheel as an integral part of the hub, and the sprockets just slide on and off.
Main advantage has been the moving of the bearings further out for the hub, and also easier to change gearing ratios.
To be honest, if you don't know the age miles that freewheel has done, I would just replace with a new one and chain. Under £30. You will need a freewheel remover, which is either splined or slotted.
For us to know, you would need to remove the wheel from the bike,clean the crud off the end of the freewheel, and if you look between the hub and freewheel, there will either be a number of splines, but I suspect there will be two slots cut into the body given its a five speed, meaning its old.