If its pre-terminated, you'll need a 16mm bit. Pretty sure this is the spec of Cat5e RJ45 connectors. I've just been routing several cables through walls and every time a 16mm bit was needed.
But if they're not pre-terminated its much easier, 6mm for standard Cat5e.
Your best bet is to buy some cable grommets like this:
And drill the hold based on the size of the tube. If pre-terminated, simply use a stanley knife to open up one side of the grommet so that you can place the cable through it, and voila. Then seal up behind it with some silicon sealant.
Oh, and if drilling to run externally, make sure you drill downwards from inside, or upwards from outside.
Edit: TheCraig - I see you want two non-terminated cables. Well you can probably force two through a 10mm hole but you might crush/damage something inside it, I'd use 12mm (if its standard Cat5e), or better yet I'd measure the width and then work to that..