Wow! Let me first commend you on being a GREAT wife to go out and get your husband a FR500 racecar. Sounds like a pristine car being only used as a show car.
There are several different models of this vehicle which were developed in the early 2000’s, FR500C which had the 5.0L engine, FR500S which had the 4.6L engine and the FR500GT which has the 5.0L engine. Miller Motorsports in Utah was the motivation for the FR500S and was used in their driver training programs. I am sure your husband will have a blast with any version.
https://www.cjponyparts.com/resources/mustang-fr500
https://en.wikipedia.org/wiki/Ford_Mustang_FR500
Be sure to have ALL fluids changed (oil engine and transmission, brake fluid, engine coolant and gas drained) before taking to the track. Likely need new tires and engine belt(s) as well as age will affect the rubber compound. These solid-axle Mustangs were the early versions of the later very popular Boss 302S and 302R versions. They are all turn-key racecars from Ford SVT and great fun to drive.
As far as a NASA contender, I am not sure. Believe NASA brackets cars by horsepower/weight. Not sure which class the FR500X would fall into and it might be competitive although suspension geometry and tuning have improved significantly over the past 20 years since that car was born. Hope this helps a bit.