Having been inspired a few years ago by Ric5's conversions, and looking for a lighter bass to take over from my Burner, I decided to go a step further, and start off with 4-string bodies but have the necks made for me. I did two basses, one chambered, and they worked out great.
I used Schaller 2000 5-string bridges on both, to achieve a 16mm string spacing. Apparently these bridges are no longer available, which is a shame because they're fantastic. The necks on both basses are pretty thin (23mm at the 1st fret from front to back), but use a 5-piece construction along with carbon fibre rods so they're really solid, with 45mm nut widths on both, 7mm front dots and 3mm Luminlay side dots. I also used tiltback headstocks for the string tension, and had the B tuner positioned a little further from the nut than usual, as I've had problems in the past with 5-string basses and the tuner being too close, so it requires you to wind some of the "speaking length" of the string around the tuner post.
The one on the left started as a 1-piece pre-routed ash body from Guitarbuild in the UK. I had a walnut guard made to hide the top rout. It has a BassMods 35AP 3-band preamp (wish they still made those too!), with Kent Armstrong Claymore pickups, which each run through mini switches so I can coil-tap and have the option of series/single/parallel on each pickup, an idea I took from the Fender Roscoe Beck V I used to own, which was a very versatile bass.
The bass on the right is a chambered custom body from Guitarandbassbuild.co.uk, rear routed control cavity, using the same pickups and switching system, but coupled with a Noll TCM-3 preamp and PA1 booster as I found the preamp by itself a little quiet. This one was made to see if I could get an instrument even lighter than the first, which is a very light bass, and to be honest, it didn't work!
But its still a fantastic instrument.
If anyone is thinking about going this route, I can totally recommend it. The actual dimensions of a "Fender" 4-string neck can completely accommodate 5 strings, and even though I had my necks built for me (mainly because I have small hands), I'd have no problem using a Fender neck with a 44m nut width on it, such as the Roger Waters Precision, and just add a tuner. My two basses are now all I use, and its good to know that if anything happens, I can put another together using 4-string bodies.