Welcome, that's a fine list!
The problem for me is the budget is all over the place, B&W 702s2 v the 805d3 they're worlds apart, and require very different levels of power. Despite what the spec suggests 805's are very power-hungry and really need something, shall we say, a little special to get the best out of them. The other problem is they're all very different speakers in terms of sound. Do you want bold and exciting, smooth and laid back, or is all about the bass!
And I don't care what, What hi-fi says your amp has not got the grunt for the ATC's 19's, you want 200 watts a channel min to really enjoy these speakers. I had them on home demo with some very nice amplification and none of really had the volume to drive them. And don't be fooled even though they're a sealed design they need plenty of room round them not to mention some quite substantial stands, think Partington broadsides they are VERY heavy speakers. With the wrong amp they do sound "lifeless and boring" as some one mentioned.
Id say just because you have 5k to spend doesn't mean you have to, The rest of your system is all price appropriate, you're about/thinking about spending almost 3 times the amount of your amp on your speakers. The 5k speakers in that list are going to up show up everything downstream warts and all.
Spending as much as you can on your speakers is flawed advice, especially if you have no desire to change anything downstream.
If it were me I'd actually be looking to spend no more than 1600 quid + or - a ton or 2 you'll have a much happier life!
Places to start
Kef r series
q acoustics concept 40's
Revel m16 f35 if you want something really special the m106 (about as good as get at this level)
Butchart audio s400
Neat alpha series
If you want something loud and exciting Klipsch heresy 4's ( really won't matter about power here, 2 watts will rock your world 100 watts well you get the idea but they sound lovely to boot)
Its great having a long list but the dealer is never doing to have all the brands
But! this is all just advice and we can't tell you what to buy just have fun AND stick to a budget.