GFCI breaker trips after 5 or 6 minutes with nothing plugged in
Change the GFCI breaker. These do have a lifetime.

EDIT

The other possibility is that a receptacle  (less likely a switch) on the circuit has gotten wet and is leaking to ground. Recently I had a roof leak into an exterior wall leak onto an external receptacle and trip the GFCI. Going off half cocked I replaced the GFCI breaker with another I had on hand. No effect. Only then did I remember that there was one never-used exterior receptacle on the circuit. I went out to examine it I saw water running down the wall from a leak around a plumbing vent.

I needed the circuit in operation immediately so I removed the receptacle and wired nutted the hots and neutrals and put a cover plate on the box. This stopped the tripping. I repaired the roof leak later.

If you think you have this problem, remove the cover plate on a suspected receptacle and direct a hair dryer into the box to see if the tripping stops.