Based on your description, my best guess is that your neck has some backbow. You need to verify this and add some relief (loosen) to the truss rod.
If it is buzzing within the first 5 frets the neck is typically too straight. If it's buzzing around the 12th, it's got too much relief.
SBMM Ray35, Ibanez ATK300, Fender Modern Playa Jaguar, Squier VM Jazz V, Mesa Walkabout Scout