I doubt that regular drill bits are meant to be used in a router.
For holes for mounting drawer slides I use the 5mm bit that is part of the LR32 set with 5mm Euro screws (Lee Valley) to mount the drawer slides. All of the slides I have used in the last 5+ years have two sets of holes, one for the typical #6/#8 pan head screws that are (sometimes) supplied and another for 5mm screws which are quite a bit beefier.
The Euro screws are PosiDrive so the Blum or similar driver (or the PosiDrive bits in the Centrotec sets) are nice to have as well.