Can I record a 6-hour video continuously by using iPhone5?

The battery has a runtime capacity up to 3 hours using the camera only. From what memory serves, the amount of runtime for the camera roll is limited up to 1-3 hours of continuous recording before the camera stops and an alert pulls up saying you used up the memory on the camera roll.

Despit that you have a 16,32,64 GB flash storage, the camera roll is limited. So it's best to offload what's on there when its full into your computer and delete it. Then record more.

No, you won't be able to do that. Figure an hour of recording consumes about 5GB's of space, and your phone, with absolutely nothing installed, only has about 13.6GB's of free space. Thus, the most you could record is about 2 and 1/2 hours.

That will give you about 4 hours of recording time, give or take a few minutes.