Wow
... and I thought my RX-8 had oil consumption issues. I had to add about 1/2 a quart in between oil changes and I thought that was a lot. I would notice the tailpipe turning pitch black over time.
Over 5 quarts without a trace of oil around the engine bay, smoke or on the ground means there was very little to begin with. Period!
Some of these "Jiffy Lube" type places don't exactly have the brightest "mechanics" around. OP, why you would trust your $40K sports car with a kid who makes $5 an hour is beyond me. Honestly, its easy enough to do yourself if you wanted to save money. AK has a great DIY on this forum if you want to learn.
I understand why you wouldn't check the dipstick, but that doesn't mean its Nissan's fault because the car didn't warn you. It's a machine, not a babysitter. You can go after the car wash place
, but you will likely have a hard time finding any credible evidence to support your case.
My dad always told me to check under the hood between fill-ups. This is the very reason why you should. It sucks that this happened to you, but at least you got a good lesson from it. Good luck. Your gonna need it.