The G500 and 550 are modern Gulfstream Vs.
They have been modified for military purposes by the RAAF, USAF, Italian Air Force, RoSAF and Israeli Air Force.
For military it is mostly used for Electronic warfare and SIGNIT and would make a great edition to the military aircraft family.
For civilian usage it would just be a shorter member of the existing Gulfstream family.
My suggestion for how to make the G500 / G550 work for military usage in game is:
Convertible into Military model (C-37B(image 1)) it can receive advanced customisation into the following:
EA-37B (image 2)
MC-55A (image 3)
G550 CAEW (image 4)
NC-37B (image 5)
