https://en.m.wikipedia.org/wiki/5D_optical_data_storage

The "5-dimensional" descriptor is only a marketing term, since the device has 3 physical dimensions and no exotic higher dimensional properties. The fractal/holographic nature of its data storage is also purely 3-dimensional. The size, orientation and three-dimensional position of the nanostructures comprise the so-called five dimensions.

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Further down in the article it is a little clearer...

In this case, the 5 dimensions inside of the discs are the size and orientation in relation to the 3-dimensional position of the nanostructures. The concept of being 5-dimensional means that one disc has several different images depending on the angle that one views it from, and the magnification of the microscope used to view it.

The website even lists a little more...

In order to increase the data capacity of optical storage, there is the potential of storing more than one bit in a single voxel by implementing multiplex technology. The recently developed 5D optical storage technique uses birefringence as an extra degree of freedom – the property of a medium whereby its refractive index varies depending on the polarization and direction of incident light. Birefringence generated by the orientation and size of optical nano-gratings offers two extra dimensions, providing much higher storage capacities.

So, it's supposedly three dimensions of position plus angle and (maybe?) polarity. So, it seems to be more than just a marketing gimmick, but I can't find any information about the resolution of those additional two parameters, so I can't tell if a single voxel stores two bits or two terabits.

The extra dimensions are time and inception. I now know less about it than when I started.

So, as I understand it, and I don't, 5D is just fancy marketing due to the really weird properties of the crystals used to store the data in. They are just calling properties of the crystal, dimensions.

I found the wiki page on it https://en.wikipedia.org/wiki/5D_optical_data_storage

According to the University of Southampton:

The 5-dimensional discs [have] tiny patterns printed on 3 layers within the discs. Depending on the angle they are viewed from, these patterns can look completely different. This may sound like science fiction, but it's basically a really fancy optical illusion. In this case, the 5 dimensions inside of the discs are the size and orientation in relation to the 3-dimensional position of the nanostructures. The concept of being 5-dimensional means that one disc has several different images depending on the angle that one views it from, and the magnification of the microscope used to view it. Basically, each disc has multiple layers of micro and macro level images.[16]