Plywood under laminate?

Hi,

My floorboards aren't the best and creak a bit. Some have been cut to get access to pipes and cables and I don't think I'll stop them all creaking unless I replace every nail with a screw!

So I've bought some 8mm thick laminate flooring and some 5mm fibre board underlay, but I'm thinking about putting plywood down first because if I screw it to the floorboards it might stop them squeaking.

Is there anything wrong with doing that? (other than the cost)

If not, what kind of plywood do I need and is 5.5mm thick enough?

Thanks!