The drop was largely attributed to a decline in the number of long-term unemployed workers, which in May totalled 67,000 people, of whom 40,000 were men, down from 104,000 a year earlier.
A total of 234,000 people were out of work last month, compared to 256,000 in April.
The workforce meanwhile consisted of 4.22 million people, statistically unchanged from a year ago.
In May, the number of hours worked amounted to 137.4 million per week, compared to 136.2 million 12 months earlier.
Sweden has since April used the European Union’s harmonised method of calculating the jobless rate.