I just bought a Z5 for my first mirrorless camera. I take a lot of portraits and artistic nudes, what is the best lens for portraits with it? Thanks.

Throughout the years the 85mm has been my favorite. I have had many different versions of it and loved all of them. I prefer prime lenses. I also have a Zeiss Otus which I love but seldom use it after acquiring the new f1.2 85mm Nikon. If budget restricts the selection maybe pick up a clean used lens.

There really isn't going to be a single "best" lens for that overall, as many aspects of that are going to be affected by how you like to shoot.

To offer more useful insight, the big questions here are:
1) How do you like to compose your shots?  From looking at your portfolio, it appears you're usually doing 3/4 portraits or tighter, but I don't know if you're planning sticking with that, obviously.
2) What perspective do you want to have on your subject, or, in coarser terms, how far away from them do you want the viewpoint to be.  (In reality, there is no such thing as "telephoto compression" - only distance to subject.)  You don't seem to have a clear trend in your portfolio images on that matter.
3) How much do you care about pure image quality?
4) How intense will your light source(s) be?
5) How important is bang-for-the-buck?

To start narrowing things down, based on the available knowns:
A) If you just got a Z5 now (and not something higher-tier or more recent), we can probably assume you care about bang-for-the-buck.
B) As most of your images appear to be very lightly processed, you probably care about image quality a good deal - this would then limit the choices to nicer offerings, such as Nikon themselves, Sony (there are good adapters for FE lenses to Z), Viltrox LAB series, some Sigmas (via the FE adapters), etc...
C) If you're asking this, it's probably a sign that you're not just coming over from F-mount Nikons (because then the sane option would be to stick an F-to-Z on, for now - unless you're using screw-drive lenses, especially since the one mount adapter that supports that has ... issues).

From what I'm seeing and/or extrapolating, I'd suggest going with a used Nikkor Z 85mm f/1.8 S from a reputable reseller such as Used Photo Pro, where I know those tend to sell for a little over $500 in very good condition, especially when they're having a sale.  That lens will focus *just* close enough (versus field of view) for the face shots you like to do, has excellent optical performance relative to its used cost, is fast enough for most lighting situations, will work well with eye-detect, won't require mucking around with a mount adapter, splits the difference on working distance options, and, finally, takes 67mm filters, which are non-exotic and not overly expensive.

All that said, I strongly recommend using something like PhotoPills to check field-of-view and related things regarding any lens you're considering before buying it and, of course, understanding its strengths and weaknesses via reviews.  (I find the ones at Photography Life to be most useful.)

TL;DR: My guess is Nikkor Z 85mm f/1.8 S.

If you don't have a regular need of shallow DOF, the 24-120 f/4 is a surprisingly good and very versatile lens.

Budget?

How do I say this tactfully...

I'm afraid that he's not in the market for any lens of any kind.