It doesn't matter what colors you select. Our eyes will see a 1/32 intensity change for one color channel with the other two color channels kept fixed when you look at the display during the color change (100%, 100%, 100%) -> (97%, 100%, 100%) or (97%, 100%, 100%) -> (100%, 97%, 100%). Depending on the values of the other two color channels, most people will not be able to memorize the color in absolute terms so if they look away during the color change they will most probably not notice the color change.

The next thing is that our eyes are exponential, so even if being able to step 1/1000 (10-bit/channel) it is very visible if changing from 1/1000 to 2/1000 or from 10/1000 to 11/1000 - but we can't see 999/1000 -> 1000/1000. This of course assuming that the surrounding light isn't too high - the eyes spans a huge intensity range but the full range is not available at the same time.

It's also important to separate the visibility of a single intensity step from the visibility of the individual steps when doing a multi-step walk from one color to another. If stepping through the color ramp fast enough, we will see a smooth gradient even if the gradient steps are large enough to clearly see if stepped slowly. When viewing a color toning on the cinema, the frame rate is very low so there is significant color changes from frame to frame. But our brains sees it as a continuous change. Even two intermediate colors is enough to fool our brain into thinking it was a continuous transition.

So 5 bits/channel works well for info signs and illumination, but you need more colors (true colors, or temporal or spatial averaging) for full-color photos.

In this case, 5 bits/channel would be a huge improvement of Chicos design since the goal isn't to display photos - at least what we know right now ;)