The prong type freewheels are about the worst design you can imagine. The tool doesn't engage well and the freewheel body isn't strong enough to withstand the torque needed for removal. Both the tool and the body often shear off.

What you are looking at is a destructive removal of the freewheel. In a nutshell, you have to remove the lockring (the inner ring with the two indentations), remove the outer shell and clamp the rest of the body in a vise. The hardest part is removing the lockring. It's reverse threaded and the indentations don't give you much purchase on the ring. It can be done but it's not easy.

Alternatively, you could just replace the whole wheel and freewheel. Wheels aren't that expensive nor are freewheels, although 5 speed freewheels can be hard to find. It's certainly a lot less hassle.