The most ergonomic and comfortable 5-holer I've ever played was the Carvin (Kiesel) Brian Bromberg 5 string signature. It's more or less like someone took a Jazz dimensioned 4 string neck and widened it only just enough to add the B string. Meaning, when you play just EADG, it really still feels like a Jazz bass neck.
That was the only 5 string I've ever played that was actually like that.
The drawbacks are that a new one is in the upper end of your price range if not a little over, and it'll take the usual until-the-heat-death-of-the-universe to get one made. I don't know if the corona virus has slowed down Kiesel's production any more than it already is, but you'd be waiting quite a while in either case.
I bought a BB 5 string "S" model, right when they first came out, with the humbucker pickup option (my bass now deceased, may it R.I.P.). It was easily the most comfortable bass I've ever played, much less the most comfortable 5 string, and I'm a big fan of the Jazz Bass style 4 string neck....
L
That was the only 5 string I've ever played that was actually like that.
The drawbacks are that a new one is in the upper end of your price range if not a little over, and it'll take the usual until-the-heat-death-of-the-universe to get one made. I don't know if the corona virus has slowed down Kiesel's production any more than it already is, but you'd be waiting quite a while in either case.
I bought a BB 5 string "S" model, right when they first came out, with the humbucker pickup option (my bass now deceased, may it R.I.P.). It was easily the most comfortable bass I've ever played, much less the most comfortable 5 string, and I'm a big fan of the Jazz Bass style 4 string neck....
L