I'm no expert on this, but I've learnt quite a lot recently from a book I got for my birthday - "Guitar Player Repair Guide, 3rd Edition" by Dan Erlewine. It's even got a DVD (which I believe might cover some of this) that I haven't watched yet.
Assuming that all your frets are ok, level, etc, I suspect you might want to be looking into "neck relief", the curve of the neck that you can control with the truss-rod.
I'd always believed that I needed a completely straight neck, and I was suffering from the same sort of thing as you describe on my Baja Telecaster after I straightened the neck a bit when I put heavier strings on.
I like what I believe to be a slightly higher action than some, but to get rid of the fret buzz around the 5th-7th frets (specially on the 3rd string), I had to raise the action higher than I wanted.
Dan Erlewine is a believer in some neck relief - ie, neck shouldn't necessarily be completely straight (and he admits many disagree with this). After some fiddling, I discovered that he seems to be right - a bit of curvature on the neck let me have the action I wanted, intonation ok, with less buzzing. I'm still getting some buzz, but it doesn't come out of the amp and isn't affecting tone as far as I can tell. (I also hit strings quite hard, and I found out that players who do this will get fret buzz that another player won't on a lower action. Obvious really, but I'd never thought about it!)
I'm sure a "proper" set-up by a luthier might get me a better result - but I quite like being able to do it myself. The only thing I won't touch is frets.
I don't feel too confident about suggesting technically what to do though - I'm happy fiddling with my own guitars, if I bust them then I bust them, but I'd hate to think that because I wrote "just yank that bit about a bit" then someone else managed to bust theirs!
For someone prepared to fiddle like I do though, I really would recommend this book - explains the consequences of what you might be about to do, making you confident enough to give it a go or say "leave well alone".
Hope that helps.