I would agree that if you were to spend stupid money - just get a real 70s Fender.
Why not buy a Fender? Fender makes THE Jazz Bass. I am just not a boutique bass fan, especially really expensive copies of Fenders. If you want super goober OCD attention to detail get a Custom Shop. But personally I think they're for tutu wearing ... whatever.
Seriously, try it first whatever you get. I have played vintage 70s Fenders that i didn't like the sound of feel of at all. And others I loved. Each one is an individual and each one sounds different.
Out of owning a 74 P, 62 RI Jazz USA, 62 RI P MIJ, and extensively playing a 78 P I like my $400 Japanese model best. Find one that plays great first, then if you don't like the sound change the pickups (with other stock sized pickups of course).
The OP is looking for a 5 string.
Also, remember that the inconsistency of the Fender basses in the 70's (which you allude to above) was IMO one of the major drivers of all these boutique instruments catching on. While I've played a few great 70's J's, I've played just as many dogs (uber heavy, dead spots, thin on the low end, etc.). I've actually played some VERY nice new MIA Fender passive four strings lately, and these are IMO a better bet than a 30 year old model from a very 'iffy' production era.