Just wanted to jump in here and mention that nothing in the FAA rules require notification, or a flight plan, before each and every flight within the 5 mile range. Rather, the rule (which itself isn't actually a rule - its a restriction on FAA rulemaking), says:
"When flown within 5 miles of an airport, the operator of the model aircraft provides the airport operator and the airport air traffic control tower (when an air traffic facility is located at the airport) with prior notice of the operation."
Although I'm not an expert (and may be wrong), my reading of "the operation" of which you must give "prior notice" is the fact that will fly "within 5 miles of an airport" at some time in the future. Nothing in the rule requires notice for every flight, or a certain amount of time in advance of the flight. The FAA certainly knows how to write a rule that requires such things, and has presumably done so in rules that require flight plans and the like for manned flights. So, it should be sufficient to send a letter to the airport and ATC that simply says "I fly model aircraft for recreational purposes. On an itinerant basis in the future, I will be flying within 5 miles of the airport. I'm giving you notice per AC 91-57A. If you have any questions, please call me at (number)."
If the airport or ATC requests additional advance notices, I think you should give that as a courtesy. Also, if you're seeking to fly in airspace outside of Class-G airspace (which you'll find a lot of near airports), you may well be required to obtain ATC permission. However, there's a lot of class-G airspace within 5 miles of airports, especially small ones. Also, I'm finding that many airports are nothing more than gravel paths on a ranchers property that haven't been used in the 10 years since Grandpa died. Some have told me that they don't want any notices. Others don't answer the phone. At least one was disconnected.
Going back to "the rule," the only rule that I can find governing UAS is 14 C.F.R. 101.41-101.43. All that is says is that you cannot fly your UAS in such a way that endangers the national airspace.
With respect to the FCC licensing requirements, it would seem that the every aircraft station is automatically licensed ("licensed by rule") to operate an airband radio unless they are flying in an aircraft that is legally required to carry a radio AND they are making flights internationally. See 47 C.F.R. 87.18(b) and this...
http://wireless.fcc.gov/releases/fcc96421.pdf
I know that some others have suggested that since you're not in an airplane, you're a "ground station," but the FCC generally thinks of ground stations as "fixed" operations, like the radios in a control tower and the like. Here's a list of authorized "ground stations":
FCC: Wireless Services: Ground Stations: Services: About
Given that, I'm not sure that you could even get a license as a ground station.
Because you're controlling an aircraft and communicating with ATC in your capacity as an aircraft, I'd argue that you are constructively "on-board" an aircraft and operating according to the license by rule - particularly if ATC has instructed you to contact them using the radio.
I also think that this is going to fall into the category of "who gives a s**t." The FCC isn't likely to even know or care about this kind of usage as long as ATC has asked you to contact them by radio. If they tell you NOT to contact them by radio and you keep doing so, this will be one of a long list of violations that they'll use to fine you..