OLYMPIA, Wash. — Washington’s unemployment rate dropped to 5.8 percent in September, the first decrease in five months.

The newest numbers are an improvement over August’s rate of 6 percent, which was the highest level in nearly four years.

Nearly 187,000 people were unemployed and seeking work in the state.

Washington added 28,100 nonfarm jobs from September 2007 to September 2008, a growth rate of 1 percent. Jobs nationwide shrank by 0.7 percent in the same period.

Government jobs in Washington dropped by an estimated 11,600 last month. Other industries that saw the largest declines were goods producers, down 3,600 jobs; construction, down 2,200; professional and business services, down 1,500; and manufacturing, down 1,400.

The biggest job gains were in education and health services, up 800 jobs, and publishing services, up 600 jobs.

Mary Ayala, chief economist for the state Employment Security Department, says that while Washington’s economic growth rate has slowed, its economy is better than it was during the 2001 recession. During that time, Washington’s employment level declined for 20 consecutive months.