how to cut glass 2mm thick and 5mm in diameter?

Answer 1

Cutting from flat plate glass a disc that small in diameter will be difficult at best. If you have the patience I suggest cutting a polygon as close to your finished size as possible and hand grinding it to final shape. You can use a medium grit wet or dry emery paper with water, backed against a flat rigid surface like another piece of glass. If you need several pieces and you can find someone who does stained glass as a hobby or small business you might be able to buy a piece of glass rod 5mm in diameter and have them cut slices from the rod and polish them to the thickness you want. (I'm assuming you don't want to spend the money to buy a lapidary saw and lapping equipment.) If they are still in business a company called Edmond's Scientific used to sell optical flats in various diameters and thicknesses.

Answer 2

if you are making a hole, use a diamond drill

If you are making a tiny disc....Why would you???