If you are operating your drone under the Special Rule for Model Aircraft (e.g. flying your drone for recreational purposes), then yes, you must contact any airports (including heliports and sea-based airports) and air traffic control towers within five miles of your proposed area of operations.
If you are operating your drone for other than recreational purposes pursuant to the new Part 107 drone rules, you are not required to notify airports within five miles of your planned flight area as long as you comply with the Part 107 airspace restrictions. In short, if you are flying your drone in Class G airspace (which includes the airspace around most small airports that do not have an air traffic control tower), then you are fine as along as your drone operations do not interfere with the “operations and traffic patterns” of the “airport, heliport, or seaplane base.”
If you are operating a drone under a Section 333 exemption or a public COA then you will need to follow the specific terms of that exemption or COA.