Karim Benzema -- Real Madrid Superstar Rents Lambo in Miami ... for $5k a DAY

Missy Elliott isn't the only rich person drooling over the new $380,000 Lamborghini Aventador -- TMZ has learned, Real Madrid stud Karim Benzema recently rented one in Miami ... for $5,000 A DAY.

Sources tell TMZ, 24-year-old Benzo picked up the hot new Lambo (in white) from Lou La Vie Exotic Car Rental on June 28th -- and drove it around Miami for a week ... partying all over the city, hitting up the usual hot spots ... LIV ... Mansion ... you name it.

But he didn't drive THAT much -- we're told Benz only racked up 180 miles on the car in 7 days ... way below his daily 50-mile allowance.

All told, the rental cost $35,992.75.

FYI -- Benzema's one of the highest paid soccer players in the world. In 2009, he signed a 6-year deal with RM worth a reported $50 million.