What could cause dizziness with right eye crossing, lasts about 5 minutes?

Anything: Any number of things could cause this. The fact that it lasted a couple of seconds requires you see your doctor for a work up.

Could be serious: Dizziness and eye crossing localize to the brainstem. I would see your primary care doctor immediately. Though it could be a complicated migraine, more serious neurological problems like a blocked blood vessel or growth in the brain need to be ruled out.