F-5's were not white. T-38s were and mostly are white. Same basic bird, but the F-5 was a real fighter, with 20 mm revolver style cannon. Not much used in USAF service, except the aggressors, but it was the F-16 of it's day in terms of export sales. Most were painted the same as any other USAF fighter of the day, although the aggressor bird were painted like Soviet fighters, right down to the numbers on the fuselage.
There is also the AT-38, which is a T-38 with a HUD and able to mount a gun pod, or other equipment to allow lead in to fighter training. Cheaper to operate than front line fighter, and it frees them up for killing Jihadies, or whoever else needs killing. We have lots, because not all USAF pilots ever get to fly the T-38 in undergraduate pilot training. The Tanker/Transport/Bomber bound folks use the T-1A Jayhawk(modified Beech 400A), while the fighter (and IIRC B-1) bound folks still go through the T-38. All fly the T-6 Texan (or T-37 Tweet, I think if they aren't all retired by now)
All USAF T-38As and AT-38Bs are being converted to T-38C standard, with modern avionics, GPS, HUD, etc.
After the B52, they must be the oldest birds in the fleet.