South Florida’s hotel market improved slightly in May, particularly in Broward County and the Florida Keys, according to new figures from Smith Travel Research. Booking rates stayed similar to last year’s in Broward and the Keys. But room revenue dropped 13 percent in those two areas and 24 percent in Miami-Dade County. Room rates in Miami-Dade fell 13 percent in May year-over-year, to $135 per night. In Broward, room rates dropped 10 percent to $105 per night. But May was not significantly worse than April, according to the data, which South Florida tourism professionals see as a positive sign.