It was in NM right? There are all kinds of bases there. I'm originally from West TX so I spent a lot of time in NM on vacations. Seems every town has an Air Force base.
Yea, we have an Air Force base in town. I see the fighter jets all the time, almost always in threes. I've never seen them flying at such altitude or in group of six though.
It's an exercise. The best is overseas when multiple forces, multiple squadrons launch two across as quickly as is safe. And lucky me was on the runway taking pictures. Years ago though. My favorite subsonic feeling and loud fighter is a launch of F-111s on full afterburners. You can feel them from a mile away. Modern stealth = quiet engines.