Given the differences in tail fins (note the little flat surface at the top), I wonder if that is indeed a T-38 . . .
Navy does not operate any T-38s as Adversaries although Test pilot School has a handful of Orange and White ones. However, in the early days of TOPGUN, the CO went scavaging and found some early A model T-38s that the Air Force didn't want and impressed them into service alongside their A-4E Skyhawks. When the first F-5E/F-5F aircraft showed up later, a few T-38s were given to VF-43, but they were retired before the arrival of the F-16Ns.
Since the T-38 and F-5 were both Northrop products developed from same common fuselage, wings, engines, etc. but F-5E and F model as well as short-lived G have distinctively different noses with radar and gun(s). The F-5 series even evolved the nose even further to the current mako shark looking configuration.
F-5F and F-5E on VFC-13 flightline. Note similar nose congifurations and compare to T-38 which is rounder from frontal view and more curved on bottom when viewed from the side.
Frontal view. (Note: Small side blisters identify former Swiss aircraft)
HJ photo