* Unemployment rate - 5.1 per cent versus 5.5 per cent in April

* Underemployment rate (employed people seeking additional work) - 7.4 per cent versus 7.8 per cent

* Employment rose 115,200

* Full-time positions rose 97,500

* Part-time employment rose 17,700

* Participation rate (people working or looking for work): 66.2 per cent versus 65.9 per cent

STATE UNEMPLOYMENT RATES:

NSW - 5.0 per cent in May versus 5.5 per cent in April

Vic - 4.8 per cent versus 5.5 per cent

Qld - 5.4 per cent versus 6.1 per cent

SA - 5.8 per cent versus 5.7 per cent

WA - 4.7 per cent versus 5.0 per cent

Tas - 5.7 per cent versus 6.2 per cent

NT - 4.5 per cent versus 3.8 per cent

ACT - 3.6 per cent versus 3.4 per cent

(Source: Australian Bureau of Statistics)

Australian Associated Press