San Diego’s unemployment rate fell to 5.8 percent in May, down from a revised 6.1 percent in April, and below the 7.1 percent rate of May 2013, according to the state Employment Development Department.

The jobless rate was also below both California’s seasonally adjusted 7.6 percent unemployment rate and the national rate of 6.3 percent for the same period.

Over the past month, the region added a net 5,100 jobs to bring the total nonfarm employment to 1.34 million. The sectors making the largest contributions to the gain were leisure and hospitality, which added 3,900 jobs, followed by five other sectors including construction, up 1,000 jobs.

For the 12 months to May 2013, the region added a net of 29,300 jobs to local employer payrolls, or 2.2 percent. The three sectors adding the greatest number of jobs were leisure and hospitality, up 6,200; construction, up 5,000; and professional and business services, up 4,800.

Five other sectors showed net job gains, and only two had net losses: financial activities, down 1,000, and information, down 200.