For bird shots (where focal length of the lens plays a huge part), I can't see how how it can be any sort of a real upgrade.
There are no suitable native Z mount long focal length lenses (and who knows when they will inevitably appear in this climate - could be half a dozen years ? Canon has their new 600 & 800mm f11's ! as competitive impetus, but whether they are going to be useful for birds, especially BIF is unknown at this point), so it will be adapted F mount long lens on any Z5 for the foreseeable future.
The main drawback as far as I can see is that you lose resolution/focal length by not having the crop factor of the D7200.
Both cameras are 24MP, but your 400mm lens (say) gives a 50% larger 600mm size image on the D7200, etc. Photographic dynamic range also favours the D7200 by the time you have cropped a Z5 image to the same subject image size.
The D7200 shoots at 6fps (and 7fps in 1.3x in-camera crop mode which I find very useful) vs 4.5fps of the Z5.
AF is another area to consider. I haven't heard reviews of the Z5's performance yet, but it think it is likely to have a similar fiddly initiation to other Z cameras. I think on balance it's likely to prove to be another area where the D7200 comes out on top.
I think the Z5's strength is as an entry level FF mirrorless walkaround street camera, portraiture, etc.
The time to change might be one day, but I don't think it is any time soon.