There is a common conceit to treat a vector of possible properties as one (small) dimension. For example, we can make your light field hold an RGB value at each coordinate. We can alternatively interpret this as a 5D field of 3D luminance vectors or a 6D field of luminance scalars.
However, if someone writes out a set of these light-field measurements as individual measurements, they might append the coordinate vector and the properties vector into one longer point (x, y, z, a1, a2, r, g, b) and claim it is 8D. However, that perspective ignores that a real light field cannot store more than one color combination at a given (x, y, z, a1, a2) coordinate. An arbitrary 8D point cloud can represent nonsensical, sparse superpositions of multiple light fields.
And it looks like it is the idea behind that storage medium. I haven't read the paper though so I can't really comment on whether or not it is justified to call it 5D.
Also note that 4+ dimensions are relevant even in a 3D world. For example the Lytro camera really outputs 4D light fields (2D position + 2D angle). Of course, there is nothing extradimensional about that camera, it is just a microlens network in front of a regular CCD, with processing that converts a high resolution 2D image into a low resolution 4D light field.