Worktop/breakfast bar

Your best bet would be to use a circular saw to cut it, then to sand it smooth and re-varnish it if needed

I would use a jigsaw blade for a clean straight cut + would put a masking tape over over the cut before cutting, so I can set us straight edge without damaging a top surface. If the cut is wisable there is always opportunity to get laminate stripping from work top manufacturers to mach up the colour and iron it on . Thanks

Rough cut it with a circular saw and then router the last 5 mm

If you don't have a router and going to use circular saw or plunge saw only. Use the sharpest blade you have and for the first cut set the depth only to cut through laminate surface 2mm or so. After that set straight edge half mm away from first cut (just tap it gently) and set the blade depth to halfway, cut again and for the final cut - full depth. When cutting move gently and don't force saw too much. Let the blade do the job. Obviously you have to use straight edge if using normal circular saw. WD40 sprayed on the blade helps a bit. If you need to glue on edging without router you will not achieve decent result though. Good luck

Use masking tape on both sides of worktop to reduce chipping, cut with circular saw, varnish/paint (2 coats min)