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People talking about x-sync (flash photography): there is no evidence in the photos of flash having any effect, even if flash is enabled and connected (OP?) The LED penguins are lit by the LED with no ambient lighting.
It seems nonsensical to say flash, because flash problems would show up as a tiny slit way on one side and all the rest black, especially tiny at 1/5000 second.
Note how the penguins at 1/2500 has more illuminated than the 1/800 shot. You'd expect the opposite for flash.
The OP never said anything about using flash.
Nobody said anything about flash. Besides x-synch being the speed relevant for flash exposures, it also defines the speed at which the shutter curtains move I'm tandem for a rolling exposure, which can create the slit effect when the curtains aren't moving at a constant or correct velocity.