New Jersey’s unemployment rate for July inched above 5 percent for the third time this year, as joblessness in the state continued to outpace the national average. The unemployment rate for July was 5.1 percent, compared with a national rate of 4.8 percent. In New Jersey, there were 3,800 fewer nonfarm jobs in July than in June, according to data from the New Jersey Department of Labor and Workforce Development, which conducts monthly surveys of employers. Of the total job losses, there were 2,500 fewer private-sector jobs and 1,300 fewer government jobs. “The national economy was slow during July and that is reflected in our state estimates for the month,” said State Labor Commissioner David J. Socolow. “Since January, New Jersey has seen a trend of moderate job growth each month until the July estimate.” Among specialty categories, professional and business services saw the most robust growth, a rise in 2,400 jobs. Education and health services and leisure and hospitality also added jobs. Manufacturing lost 2,800 jobs, the most of any sector. Construction and financial activities also lost jobs for the month, the data showed.