Sorry for the long post but bear with me it may be useful.
Spior your confusion is very understandable. Basically you have a hinge that is for fitting with ordinary woodscrews not the 5mm ones you have.
There are two seperate issues here.
32mm system holes and mounting plates
The 32mm spaced holes (each
5mm dia) running up the inside wall of the cabinet are where the hinge plates (also called cruciform mounting plates over here) are fitted.
THIS is where the 5mm screws are used. Look at the second picture on the Rockler link and you will see the screw is on the mounting plate (It is also on a white drawer runner which perhaps shows the versatility of the 32mm system.)
There are several types of mounting plate and there are different fitting options.
System (or Euro)screws;
Expando.
These fittings all use the 32mm system with a 5mm hole. They are often used in what we call 'chipboard' because ordinary woodcrews will simply pull out as the board is relatively weak and needs a larger diameter screw to anchor the plate properly. These are used in mass produced furniture from retail outlets and by many kitchen fitters.
Knock in fittings;
These also use the 32mm system but are pre-fitted with dowels and need 10mm holes not 5mm. (More confusion

)
Woodscrews;
These don't use the 32mm system. For these fittings and you need a separate template to mark where the screws will be positioned on the cabinet sides. I tend to use this because I can fit the hinges wherever I want and I don't like a row of holes up the inside of my cabinets. (Looks too mass produced

)
The hinge is fitted into the door itself (see below) and slides onto this mounting plate and is secured by either a clip (ClipTop) or screws (Modul).
Hinges
There are Blum hinges for almost every application
http://www.blum.com/us/en/01/20/40/ with the following fitting options.
Woodscrews
Inserta
Knock in
You can try and drill the fitting holes for the hinges freehand but it is far easier, more accurate and quicker to use the dedicated boring machine ECOdrill. They're not cheap but they are worth every penny (sorry, cent ;D).
http://www.blum.com/us/en/01/70/10/
There is a large 35mm hole that the hinge boss fits into. Depending on the fitting you are using there are then two more holes drilled either side of this and off-centre which are
8mm in diameter. This is where the Inserta or Knock-in fitting goes. If you are using woodscrews the boring machine can be set up to just make a small mark where the screw should go.
So to just to avoid any confusion the 5mm screws are NOT used to fix the hinge itself they are for fitting the mounting plate to the cabinet side.
Once you start using the system with the relavant templates/drilling machines it all fits together quickly and accurately but it is a bit of a learning curve to start with. Have a look at the Blum US site links above but also the UK one where the Media Centre has more information including a full catalogue
http://www.blum.com/gb/en/02/90/.
You will also need a supplier who knows the system otherwise they will sell you screws that don't fit or dowels to fit in the holes you spent ages drilling out accurately!!
Hope this helps and have fun.
Peter