We generalise previous results to dimension 5. We exploit the geometric properties of the 5-hypercube [0, 1]5 in order to give a mathematical model for colour vision in the case of 5 photoreceptor types and for the corresponding additive colour combination with five primary lights. Five photoreceptors or five types of camera pixel filters with responses normalised to the interval [0, 1] give rise to a 5 dimensional hypercube [0, 1]5 of combined responses (colours). As previously done, for the trichromatic and tetrachromatic cases, we identify an equatorial PL 3- sphere in the PL 4-sphere boundary ∂[0, 1]5 of the hypercube. This equatorial sphere is the set of hues of the chromatic colour points in the hypercube. The remaining attributes of luminance and chromatic saturation are given by the midrange and range of the colour coordinates. From the 5-cube we go to a polytopal hexcone type space, to a double-cone type space and to a round Runge space.