Auto sales were up 17.9 percent in the 12-month period.
United States auto sales are down about 6 percent so far this year from last year's levels.
The current record for auto sales, 16.3 million, was set in 1986.
Over all, auto sales were up slightly less than 1 percent for the month.
Despite the gain, auto sales were still 4.9 percent lower than last year.
European auto sales were down 17.9 percent in May, compared with the month a year earlier.
August and September were among the best months ever for auto sales.
Without strong economic growth, the outlook for auto sales is not good.
Auto sales have been running better than expected so far this year, economists said.
Auto sales tell me whether people are feeling confident enough to buy new cars.