Depends on the thickness of the metal. You may just end up with an exploded tap. With wiggling of the tap clockwise/anticlockwise into soft thinner metal, don't let it bind up and if it starts popping stop before the tap breaks. . If your tap is cheap it's far more likely to just explode. Personally I would use a good quality 5mm drill as a reamer and wobble it sideways / hold drill tool handle loosely to slightly enlarge the hole.
If you've got a 5mm drill to take the original thread out, you might get away with it if you have all three taps, a 1st cut, 2nd cut and finishing tap. Go slowly, use a cutting grease and do it by hand. DON'T stick a tap in a drill and go for it, as you will snap the tap. It's going to be really tight to start off, you'll need to be reversing the tap every quarter turn until you get through.
Basically attempts to cheap out by not spending any more may be met with more expense in taps than just buying the correct drill. You still may break generic no-name tools on it though.
I didn't suggest wiggling it like @mikedjames said, as I'm assuming it might be an engine part you're doing. Wiggling would clear the hole, but unless you have a really steady hand and can restrict the wiggle to 0.25mm, you'll end up with a weak thread.
Good point, I need to do it today though and can't find one locally, me engineering mate says 5.25 is the only drill he can't find, I have got the three taps mind
Screwfix? Toolstation? They both do cheap drill and tap sets, worth it if it's an emergency one-off, though might not last forever. The drill bit is only going to be clearing the hole, not a fresh hole in solid metal.
Hadn't thought of buying the set as I have the taps, will check it out, I doubt the cheap sets will have M6 fine though
But you only need the 5.25 drill bit. If you have the three taps already, might get you through your task.
Normal M6 is a 5mm drill, but as you said that's the coarse thread. I've had a quick look and the usual suspects don't do fine thread drills. If you don't have a specialist tool shop near you, looks like you'll have to try the slow expansion from 5mm.
If you are really rich you can buy a combined drill and tap that you put in a power tool.. great for 19inch equipment racks made from 3mm steel angle iron, made by Azerbaijani dock yard apprentices, where the frame is bowed 10-15mm by precision welding so it's just as well they weren't asked to drill and tap the holes too.
