The 59th 500 Mile International Sweepstakes was held at the Indianapolis Motor Speedway in Speedway, Indiana on Sunday, May 25, 1975. A. J. Foyt started on the pole position and Bobby Unser won his second Indianapolis 500. Dan Gurney, one of the founders of All American Racers, who finished second as a driver himself in 1968–1969, won his first and only Indy 500 as a car owner. Gurney's Eagle chassis itself scored its third "500" win. The race was part of the 1975 USAC National Championship Trail.

Robert William Unser was an American automobile racer. At his induction into the Motorsports Hall of Fame of America in 1994, he had the fourth most IndyCar Series wins at 35. Unser won the 1968 and 1974 United States Automobile Club (USAC) national championships. He won the Pikes Peak International Hill Climb overall title 10 times.