It was the lowest jobless rate since the second quarter of 2008, the Office for National Statistics said.
The number of people out of work was 1.77 million between June and August, down 79,000 from the previous quarter.
The number in work rose by 140,000, bringing the employment rate to 73.6%, the highest rate since records began in 1971.
Some 22.77 million people were working full-time in the three months to August, up 291,000 compared with the same period last year.
The number working part-time rose 68,000 to 8.35 million.
There was a 4,600 rise in the number claiming jobless benefits to 796,200 in September.