If you are flying in the US as a
RECREATIONAL pilot, within 5 miles of an airport (
towered or
non-towered), you must
notify the airport and/or ATC. You do
not need them to authorize your flight.
The only regulating body that can give authorizations is the FAA.
- Per FAA regulation, max altitude is 400 ft (with caveats around taller structures)
- ATC or the airport can tell you "No, you cannot fly". However they do not have the authority to enforce that. If you fly anyways and an incident occurs, you could be held liable for violating the airspace though.
If you are flying as a
COMMERCIAL pilot, in which you have passed the Part 107 Remote Airmen Certificate Test, you
do need authorization for towered airports aka Class B,C and D airspace.
This is given via the FAA waiver process, not by calling the tower,