Now that I have my Tri-planar tone arm, I ask for recommendations for a new cartridge.

I am thrilled with my new Tri-planar tone arm. It completes my analog rig incredibly so.
A Woodsong Garrard 301, Atma-Sphere MP-3 phono stage. Currently using a very nice Mayijima Shalabi.
I am relatively new to analog and, mostly, I know that the Japanese seem to be on top of the cartridge game.
Thinking of upgrading to the $5K price point. I listen to a lot to vocals, Classical and Jazz. Am certainly open to recommendations.
Yep, if you like the Miyajima sound you could move up to a Madake or Destiny. They'll be a good match on your arm.

Industry disclosure: I'm a Miyajima dealer.

 Industry disclosure: I'm a Miyajima dealer. 

Interesting, maybe you can help, in another thread I asked people about  Otono-Edison Standard Mature Wood MC

As you may know the Miyajima is an export brand of Otono-Edison.

In Japan the Mature Studio BE/SW equal to OP's Miyajima Shilabe.  

The best cartridge I ever heard in that price range was the
Clearaudio Stradivari V2

Enjoy the Music
Those Miyajima cartridges are very fine indeed, but aren't they low compliance?  In my experience, the Triplanar does its best with "medium" compliance cartridges.  For one example, the Triplanar never got the best out of my Koetsu Urushi, whereas it does very well with some MMs and the AT ART7.
1+ Lewm

Atmasphere has a Tri Planar. You might ask what he uses.

The Japanese comment is way off. You are forgetting about Grado, Clearaudio, Soundsmith, Ortofon, Van den Hul, Goldring and others. The Japanese have not developed anything. Joe Grado invented the MC cartridge.

 Clearaudio and some Ortofon cartridges as well as all Lyra cartridges are a great match for the Tri Planar as are Dynavector cartridges. The Ortofon Windfeld Ti is the real overachiever in your price range. Any medium compliance Soundsmith would be great. You can use a low compliance cartridge. You will just have to add some mass. Lighter systems have less distortion than heavy ones. 
The Madake has an old school cantilever with a pressed in stylus leaving unnecessary mass at the most inappropriate place, the very end of the cantilever. In comparison to a Soundsmith ruby cantilever that thing is a baseball bat. I don't care what it sounds like. It can not possibly track as well as a more modern design. For me it is a total non starter. I am also not a huge Shabata fan. I think the GygerS, Replicant 100 and Soundsmith OCL styli track more quietly. Not sure why, but that is my experience. AT's ML stylus is also excellent.  
You should learn a bit about new Cross-Ring Coil Design which is a Miyajima patent.

Bamboo cantilever is another exclussive.

The OP got his Shilabi, there are at least 2 steps up (Kansui and Madake). They are all assembled in hardwood body, different type of wood for different models.
It’s a modern cartridge, but what a cartridge! I got Kansui and all reviewers are crazy about this model, Madake is next.