Determine just what kind of paint first. If it's dull after five years, I'd be wondering why. If the paint used for the repaint was Imron, or Aluminigrip, it should have held a good shine for a lot longer than that. If one of those two, or a similar quality paint was used, you may find it hard to polish, it's just tough paint (I've got imron, and I've tried.)
If it is a softer paint, compounds will work on it. Refering to products available in North America, I prefer Turtle Wax "Polishing" Compound. I do not use Turtle Wax "Rubbing" Compound for two reasons: Polishing compound is white, and rubbing compound is rusty red colour. If you're polishing white paint, the rubbing compound will stain the white paint, and be miserable to remove. Further to that, as it is more coarse, it tends to put in scratches which are challenging to remove (particularly the red ones). The white compound is finer, and white. It will take longer, but I prefer the outcome.
After that, a good wash, then "Wax". Choose a good quality "wax" which is white in colour (assuming that most of your plane is). I once tried a product called "Rain Dance" which was blue. I had a little blue circle around every rivet, lots of work to clean off. "Nu Finish" is white, and produces a very pleasing result.
With any product use great care to not polish or rub right through the paint, particularly with soft paint. That said, if you have a really tough polishing problem, extremely fine sandpaper will work. By fine, I mean "grit" numbers more than a thousand. Preferably several thousand. This paper can be hard to find, but a source for small quantities, you'll find it in automotive headlight polishing kits. Don't sand through the paint!
As for static, I can't argue your wisdom, but I would not get too excited about this. You're probably standing on the ground, and thus grounded yourself. I also doubt that you have the personal endurance to rub enough to build up a harmful amount of static, but you can't go wrong bonding things!
A clean shiny plane is a delight, and you'll pick up a little speed... Well, it'll feel like it....