I've had a look at your website and your kit list in your profile, what are you looking to gain by buying a D5/D500 and 500mm f4 over what you already have? The kit you have is already good enough to shoot wildlife and sports, perhaps a fast longer lens may be usefully if you are shooting birds but do you know the reasons/advantages for getting it? The problem with long lenses is weight, it's a pain to carry, move and setup a tripod for each shot and something I didn't think of when I purchased a 200-400. I find I don't use it as often due to the weight and hassle of a tripod. It's a nice lens and I have good reasons for purchasing a
second hand fast aperture versatile zoom. Could I get away with a cheaper lens and get roughly the same images? I probably could, it's something I'm currently thinking long and hard about 'downgrading' as if it's not used enough then it has to go as it's an expensive item just to store and not use. If you don't enjoy using it you won't use it, it's as simple as that. I could probably get away with a 300 f4 in place of the 200-400 and use it more as I would enjoy carrying less weight and be more manvorable too. Has the 200-400 made me a better photographer? No. Has it made people comment that I must get great images as my camera/lens is big? Yes but that doesn't make my images better. I'm honestly thinking I would be happy with a light 3 lens setup (24-120, 70-200 and 300 f4), it would do most of what what it to and not kill my back carrying it all! It may actually improve my photography as I would be thinking more about the chance of moving slightly to get the better background, composition or light rather than think I don't want the hassle of setting up the tripod all over again! I use my 70-200 for quite a lot of my wildlife stuff and love using it. I just plan to visit places where it's nearly the perfect lens and enjoy using it as its relatively lightweight compared to a 200-400.
As you have said 'I probably need a decent telephoto to go with the new camera' and 'would this be a good choice?' it makes me think you are not sure why to go with these and haven't worked out a need as such, more you have heard it's what you need to be a wildlife/sports photographer. What are the reasons for deciding on a 500 f4? Could a different lens be a better option? Is weight going to be an issue (carrying 6-7kg of long lens, camera & tripod can be a right pain)?
For some wildlife a 500mm f4 could be useful but for sports it may be too long and too slow. Lots of sports photographers use the 300 f2.8 and 400 f2.8 for the fast aperture in what is poor light under floodlights and a d4/d3 as they need the fps and great buffer but this is the thing most of us enthusiast don't, we can get away with the lesser models that do 6fps and rattle off 25 continuous raw files. A 300 f2.8 with 1.4 and 2x teleconverters on the d810 would be perfect for many wildlife photographers and also good for sports. I honestly don't think you need to spend £14k+ to go out to shoot more wildlife and sports when you have good kit already. I honestly wouldn't buy a D5 or D500 when they are released, wait a year until the price drops and they iron out all of the first batch issues that always seem likely with new Nikon releases. also buying good used equipment isn't a bad idea, it's cheaper and often it's nearly like new but without the price tag. For many we won't push a D5 or D500 enough to reap the benefits of one over a d750/d810 or a d7200. Nikon/Canon/Sony/Olympus/Fuji etc have great marketing departments and are very good at selling us something we think may give us a slight advantage.
What wildlife and sports do you have in mind? Living in Pembrokeshire you are not far from skomer Island. It's a great place to go where you don't need long lens and staying overnight is much better as the light is much much better. The fact you are so close you could probably book several 2-3 night stays over the puffin season and turn it into a mini project quite easily (all of the kit you have now would be perfect too). You may be able to book quite late if they had spare beds to fill. I would love to be that close, it's a 6-7hr journey for me so I have to pre-book and only make one trip, taking a chance on the weather!
What I've said above may not be what you want to hear. Good gear does help in certain situations but it's doesn't mean your photos will get better because of it. This said if you have the money and like to spend it on your hobby and it makes you happy then why not...... just don't listen to me.
