The seasonally adjusted unemployment rate fell from 5.6 per cent in April, with employment growing by 12,000 jobs and the participation rate dropping by 0.2 points to 65.5 per cent, figures from the Australian Bureau of Statistics show.
The more stable trend rate also dropped - from 5.8 per cent to 5.7 per cent.
Full-time employment decreased 20,600 to 8,521,400 and part-time employment increased 32,600 to 3,996,900.
The number of unemployed persons looking for full-time work decreased 11,200 to 494,300 and the number of unemployed persons only looking for part-time work decreased 15,600 to 220,300.
Nationally, the unemployment rate dropped from 5.6 per cent to 5.4 per cent.
Elsewhere, the unemployment rate lifted in Tasmania (to 6.6 per cent).
"Weaker employment growth, stagnant real wages and falling house prices together make for a challenging environment for households", Ms Hunter said.
Victoria fared the best of the states, generating 22,100 jobs, and its unemployment rate dropped to 5.1 per cent.
However, WA defied the trend with the State's jobless rate edging down to 6.4 per cent.
State Industry and Skills Minister David Pisoni said the total number of South Australians in work was at a record high, with 842,600 people in employment.
In a sign of a slowdown in the jobs market since the start of the year, over the past 12 months the nation has created 303,900 jobs.