how to convert my 15 speed bike to a 21 speed.

[L33+]

I am going to buy a new chainwheel as mine is broke (still 3 cogs though)
my bike is gripshift and only goes up to 5, i am going to ditch this and buy some thumb shifters that will work with any amount of gears because they work by friction.
now am i correct in assuming that all i need to do is swap my 5 speed freewheel for a 7 speed one?

 

[gclark8]

If only you were in Australia, I replaced all my 7 speed stuff with 8, so I have wheels, derallieur, shifters, the lot and have a spare triple crank, all new.