Fret board rattling on the E string

I understand this must be a common thread here. But I just picked up a "Fender P Bass special" the other day for about $650. It is everything I could have hoped for. The only problem is, when I play the E string it rattles. I know the rattling is the string hitting the fretboard because I've tried several methods to see what is causing it. When played open the E string doesn't rattle. If I were to hold down the 5th fret or higher it does rattle. I tried tightening the bridge but that did nothing at all. How can I fix this?

Hi I dont know if you have tried any of this so apologies if its obvious have you checked that as you move up the fret board and the string gets lower that its not starting to touch one of the pickups or when you move up the fretboard is there a point wher it stops rattling move back one fret and check if that one is sitting higher than normal and have held down the string at the first fret and where it joins the body to see how much clearance there is under the string to the top of the frets about half way down there may be too much relief in the neck you can adj with the truss rod no more tha a quarter turn at a time to be safe or may be the opposite there is no relief hope this is of some help