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What about the reasons for getting a 5K monitor? Based on the answers, we see the clarity going from lower res monitors to 4K monitor. Can we tell the differences between 4K and 5K? Given that iPhone can shoot 4K rather than 5K videos, will we be able to see better quality videos when playing or editing 4K videos on a 5K monitor?

Remember, there are a few variables here. Many have addresses the fact that with say 5k you see twice as much (well, 4x) as an older 2.5k iMac. Think of photo editing: if that image was shot on your camera at 3kx5k more of it will show at 1:1 (one photo pixel for one screen pixel) on the 5k than the 2.5k, making editing easier since you see more.

But that doesn't address pixel density, or pixels per inch. A pixel is just an object, like a square. It doesn't have an inherent size. A pixel on a 70" 4k HDTV is bigger than one on a 23" 4k monitor. The former has fewer PPI than the latter. They can both be showing the same photo at 1:1 but depending on how close you are to the monitor you may see the pixels, or not. A laptop or tablet has a higher PPI cuz you hold it closer to your eyes; a Jumbotron screen at a stadium might also be 4k but with HUGE pixels and you wanna sit far from it. The whole point of retina-ness was to design a screen with a lotta pixels (high PPI) so it could show a lot of stuff WITHOUT being pixellated at close viewing distances, like the iPhone.

So yes, a 5k shows a lot more pixels than a 4k. But since many 4ks are the same size dimensionally (say 27-28") the 5k also usually has a higher PPI. Which means you can get closer to it and not see pixels. The "retina distance" for the two would be say 22" for the 4k, 16 for the 5k 27" iMac. Or 158 PPI for the 4k, 217 for the iMac. Getting closer also means your field of view changes; the 5k at retina distance would fill more of your view and so sorta look "bigger."

I say this because these factors influence your ergonomics and vice versa. Buying a 5k and then sitting farther away might be a waste; you might not be able to see the detail you paid for. We kinda aren't used to that. And Apple's retina HiDPI graphics help in that they bump up the dimensions of icons 4x so that they look the same size as on a 2.5k iMac, just FAR more detailed. And the OS is smart enough to show that 4k at 1:1 in say Premiere, but still show icons, buttons and such at a bigger size for ease of use. So a big deal with the 5k is that you can see the video without it being cropped or scaled, but still have all the controls you need. Ditto with bigger photos.
 
The main reason for 5k over 4K is if you are editing 4K video you can edit one to one pixel wise and still have space around it for all your editing tools.
 
Can the eyes tell the differences in playing 4K videos from 4K and 5K monitors?
 
Can the eyes tell the differences in playing 4K videos from 4K and 5K monitors?

Probably not - you're missing the point: You don't buy a 5k display to get better quality than 4k, you buy a 5k display to get more on the screen at "4k quality".

In terms of iMacs and the new Apple-endorsed LG displays, you're probably going to be comparing a 21.5" 4k display with a 27" 5k display. The "pixels per inch" for these are about the same, so:

On the 21.5" 4k, a 4k video will play back optimally, 1:1 scale, in full screen mode
On the 27" 5k, you've got room to create a window as big as, and with the same number of pixels as the 4k display in which a 4k video will play back optimally, but leaving room around it for your editing tools.

The other advantage of 5k is that its exactly double the number of pixels (in both directions) as the non-retina 27" iMac was, so it works optimally with the Mac's pixel-doubling "retina" mode that maintains compatibility with non-retina software. This makes 5k displays a bit of a "Mac thing".
 
...Are they beneficial to programmers, writers, and academics who run Matlab, writer papers and design using CAD, occasional use of Illustrator and Photoshop?
Yep... 5k allows me to have the browser visible on the right side of the screen with atom on the left to see codes changes immediate effects. This saves countless hours. I use Pixelmator for quick graphics work and Sketch for mockups. The larger res gives me more room to work and better assists me in seeing the 'larger' picture of the ui workflow for the end user.
 
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