There is a small private field with a single 1900 ft grass runway about 3 miles from my house.  It sits on 20 acres of ground (1/32nd of a square mile).  Does the prescense of this airfield preclude anyone from flying a DJI Advanced class drone anywhere within the 78.5 square miles of land that compise the 5 mile radius from this place?

The private field has no tower to contact, and the associated phone number goes unanswered and does not have a voice mailbox associated with it.

Same problem here. I have a small airport here with a little air traffic.

Kind of the same problem here.
AirNav's listed numbers for the operator of the airfield near me is disconnected. Not sure what to do about them, but at least I'm trying to make contact.
There is a helipad at a nearby hospital, but they never pick up the phone. I've left messages, so at least I'm doing my part.

You can fly within 5 miles of an airport but you must call to advise the airport first. Since there is no one there to call you call FAA Flight Services and the them know. These used to be local but now they are regionalized. I am sure they will get tried. But it is there rules.

Does it bother anyone else that this whole thing is pointless? How would calling some faceless FAA entity far away help inform a private pilot landing at a grass strip to watch out for low flying drones three miles north east? How would the FAA notify thousands of aircraft pilots of thousands of drone flights going on at any given moment?

Cross checking with the other post that have the geo locking maps, I'm not seeing my local airport even showing up.  That is rather strange, given that a friggen PRAIRIE near my farm is outlined in green...