5 string bass (High C)

Any 5-string will work. I'd suggest a 5'er Jazz, since thats precisely what you described. On the cheap ($150-$250), I'd suggest a Brownesville UB500. Similar to the old American Deluxe Jazz basses. If you can afford more (like $1500) You could find a used American Deluxe. Or you could get one of the many Bass VI knockoffs floating around and tune it EADGCe,, and have the extra high e as well. Rondo sells these for between $350 and $450.

 

Ummm... You don't really need to buy a specific 5 string to have a high C. Just buy any five string you want, get a set of strings with a high C, and have a tech make you a new nut if you end up liking it.

And I do have one, it's a yamaha BB415 that I put a high C string on and took the low B off, any bass can have this done...

 

Yup, any 5er bass'll do it. Sounds like you want a 5er Jazz.

It's an incredibly fun tuning, IMO.

 

I had my old Spector Legend strung EADGC
no new nut was necessary
and I just bought a cheap D'Addario 6 string set and was good to go
considering that the Spector was already good for the higher notes, chords and lead playing was a breeze and cut through the mix

too bad it was 35" scale and my hands couldnt get used to it