The slight job growth followed a stronger month of April, when revised numbers show a gain of 8,900 jobs, the state Employment Security Department figures show.
"This is the lowest monthly job gain so far this year," Paul Turek, a department labor economist, said in a written statement. "Meanwhile, our workforce grew, but the unemployment rate stayed the same because the proportion of job seekers who got work about equaled those who did not."
Two different surveys are used to calculate unemployment figures and job losses and gains.
The unemployment rate represents the percentage of the labor force that is unemployed and actively looking for work. People who have stopped looking for work are not counted. The job gains and losses estimates are based on a U.S. Bureau of Labor Statistics survey of businesses.
Turek said nearly 3.5 million people are counted among the state labor force, a figure that increased last month by 6,500 workers.
Employers have added an average of 6,560 jobs each month this year, Turek said. The department estimates that nearly 74,000 jobs have been added statewide during the one-year period ending in May.
In April 2013, the state's unemployment rate was 7 percent.
The largest job increases were seen in leisure and hospitality, retail trade and construction. The biggest decrease was seen in government, with the losses including short-term positions that had been created in response to the Oso landslide. Other sectors that saw job losses were professional and business services and manufacturing employment.
Washington's unemployment rate is below the national rate of 6.3 percent for May. State officials say the rate in the Seattle-Bellevue-Everett area remained the same as the previous month, at 5 percent.
An estimated 211,800 people were looking for work, including more than 74,000 who claimed unemployment benefits in May.