Growing bandwidth demands are driving the search for increased network capacity leading to the exploration of new wavelength ranges for future communication systems. Therefore, we consider two technologies that offer increased transmission bandwidths by virtue of their high carrier frequencies, namely optical wireless and millimeter-wave transmission. After highlighting the relevant electromagnetic (EM) spectrum region, we briefly describe the applications and properties of each approach coupled with a short history of their development. This is followed by a performance comparison in two possible 5G links: outdoor point-to-point and indoor hotspots. We find that in both cases, there are regions where optical wireless communications (OWC) are better, but others where millimeter waves are to be preferred. Specifically, the former outperforms the latter over distances up to approximately 50 meters outdoors and a 10-meter hotspot radius indoors.