You can absolutely make hi-color images which are close to visually indistinguishable from the 24 bit originals, by using a good dither matrix. GdkRgb did this

You can absolutely make hi-color images which are close to visually indistinguishable from the 24 bit originals, by using a good dither matrix. GdkRgb did this well over 20 years ago, back when "CRT" meant a display technology, and the fuzziness made the dither patterns melt. If you were doing it really carefully, you'd use a corrective gamma function, as dithering in a nonlinear colorspace is not an identity transfer function. Alternatively, you can do error diffusion in a linear space. But at 5 bits, the effect is fairly subtle.