I did some research relating to this area for:

$5$ dimensional space over $\mathbb{R}$

There isn't much to be found on the Internet other than at Wikipedia, except for:

A FAMILY OF MARKED CUBIC SURFACES AND THE ROOT SYSTEM $D_5$, by Elisabetta Colombo and Bert Van Geemen

which is detailed but has no pictures.

I did some research relating to this area for:

$5$ dimensional space over $\mathbb{R}$

There isn't much to be found on the Internet other than at Wikipedia, except for:

A FAMILY OF MARKED CUBIC SURFACES AND THE ROOT SYSTEM $D_5$, by Elisabetta Colombo and Bert Van Geemen

which is detailed but has no pictures.