You have a huge oil consumption problem and you will lose your engine if you don't get it fixed or keep checking and filling every day. Get it checked out by a Nissan or Infiniti specialist ASAP. Here's a directory link for you: http://repairpal.com/directory?address=19087&car_brand_names=Infiniti
I called an Infiniti dealer. He recommended I run the care for 1,000 miles, then bring it in. I just had the oil changed at the Nissan dealership who had been doing the oil changes, so it is full (and I just checked it, to make sure).
It was the Nissan dealer who told my wife that she needs a new engine ($9500, installed). On top of that, the "check engine" light is on. There's something screwy here. There has been absolutely NO evidence that the car is burning oil besides the Nissan dealer's say-so. There is no smoke, there are no oil drippngs on the driveway (and we just got the driveway re-surfaced this summer, so ANY oil would show up immediately, there is no smell of burning oil. So where does 5 quarts go? Personally, I think the dealer is either incompetent or a crook. I'm going to take the Infiniti dealer's advice, drive it for 1,000 miles, check the oil level every couple of days, and see what it looks like then.