Officially — at an uncontrolled airport — you're required to inform the management that you'll be flying within the 5-mile radius, not necessarily get permission. They can file a complaint if there's a problem; but given you have your cert, you're probably not the guy who's going to cause any problems.
In speaking with the manager of my local (uncontrolled) airport, he says (paraphrasing) "Fly all you want, but if you're going to be close to the approach/departure routes or spending a lot of time at altitude let me know and I'll loan you a radio so you can monitor traffic." Around here he's more concerned with pilots sightseeing below 500'...
There's an operator here locally who does a lot of work with the Forest Service, he sends the airport manager a text with the date/time/estimated duration of his flight; nature of his flight; lat/lon; operational radius & altitude. Works a charm. I fly a lot in the area — generally out on the fringes of the 5-mile radius — so we've agreed that contacting him every time would be a pain for all parties concerned.
Cheers!