Thanks for the mention hark, I appreciate the thought.
High speed photography is kinda a large subject, but with a HSS capable flash (such as the Nikon SB-600, 700, 800, 900 class), HSS should do the dancing job if the camera is on stage with the dancer, within up to maybe 18 feet, or more with high ISO. HSS is NOT a fast flash, it is merely High Speed Sync.
It is not technically a flash, but becomes continuous light, being on all the time the shutter duration is open (which looks continuous to the shutter), so continuous is the slowest possible light that cannot stop motion at all. Shutter duration has to be 1/250 second for HSS work, so it looks to humans like a flash, but it is continuous for that duration. Used because continuous has no sync concept, it always "syncs" at any shutter speed. Meaning, like any continuous light, it uses the regular Equivalent Exposures, meaning wide apertures must use a fast camera shutter speed to still be equivalent. You can switch to any Equivalent Exposure with HSS (well, faster than 1/200 or 1/250 to enable HSS). So the HSS flash is NOT AT ALL fast, but you can have the fast shutter speed to help. However, for a fast shutter speed, the lens will be stopped well down, so you won't have much depth of field. If you feel the need to stop down (like in bright sunlight requires it), you can gang 2 or 4 flashes for 1 or 2 more stops down. Each power double can stop down one stop more.
I remember the early McNally books touting Nikon HSS, and his pictures showed him ganging four Nikon flashes in an umbrella for a model in the desert sun. This need was never mentioned in words.
But indoor lighting is a different easier class.
My site at
https://www.scantips.com/lights/flashbasics2b.html explains HSS, and
https://www.scantips.com/lights/flashbasics1c3.html has a HSS Guide Number calculator. These flash model manuals in the specifications give the HSS Guide number chart, and for the SB-700 at 50 mm zoom and ISO 100 and 1/500 second, it is 46.6 (feet). My calculator will convert that to other ISO and shutter speeds and show power level for the distance and aperture. But TTL should work too if in range.
You can use the camera meter for HSS, but the Guide Number calculator can give you expectations of possible range ahead of time. The room does not need to be dark for HSS, since both the HSS flash and room lighting is continuous. HSS becomes more a fill flash for the room lighting then (but sunlight is so bright, it sort of overwhelms and needs a stopped down aperture instead of f/2.8 to expose sunlight).
Alternately, (switching to Speedlights), speedlight mode is much faster than camera shutter speed when at low power, but lowest power means the range is short, more like inches than feet (at least if stopped down to f/16 for macro work). These Nikon flash manuals (I think not the SB-500?) give the flash speedlight duration in the specifications.
For the SB-700 it is:
1/1042 sec. at M1/1 (full) output
1/1136 sec. at M1/2 output
1/2857 sec. at M1/4 output
1/5714 sec. at M1/8 output
1/10000 sec. at M1/16 output
1/18182 sec. at M1/32 output
1/25000 sec. at M1/64 output
1/40000 sec. at M1/128 output
And all models are about similar speeds, but not the same exact specifications. So they are called speedlights, because even like a normal 1/2 power is around 1/1000 second. But sunlight at sync speed can still show some motion blur.
Except for the one full power setting (which it is NOT speedlight speed), the speedlight clipping off flash duration for low power makes the others fast which approximate a T1 time, but the shutter speed still has to be 1/250 or 1/200 second to sync, Which is much slower, so that means the room has to be reasonably dim. Not necessary real dark, but a picture there at the same settings with the flash turned off or unplugged should come out black, else the room light can blur the speed. But in practice, just dim works OK and you can still see to work (but test it with that black exposure).
So about 1/32 or 1/64 second works real well for milk drop splashes at f/16, and a 105 mm macro lens keeps it far enough back (a few inches) to not splatter the lens with milk (wise to use a clear filter on it though).
Hope that is of some interest.
Wayne