Unemployment fell by 121,000 to 2.12 million between March and May, official figures showed.
The number of people claiming jobseeker's allowance last month fell by 36,300 to 1.04 million, said the Office for National Statistics.
Average earnings increased by 0.3% in the year to May, 0.5% down on the previous month.
The TUC have said that a poll of more than 1,600 adults showed that most were opposed to the five-week wait for benefits
TUC general secretary Frances O'Grady said:
Making people who have contributed all their lives wait five weeks before receiving any help is both cruel and vindictive.
Just as with the bedroom tax, it shows that ministers are desperately out of touch with the lives of ordinary people.
People who lose their jobs need to be concentrating on looking for a new one, not worrying about whether they have enough money to pay the mortgage, keep up with their rent or feed their children.
The five-week wait is yet another ill-thought out idea and should be enough to send the whole policy back to the drawing board.
Recently unemployed adults may have to wait five weeks before they get any benefit payments, according to a new report.
The report, published ahead of the latest unemployment figures, said the new five-week wait will apply to anyone making a fresh claim for social security benefits.
The union organisation said it was a "new and deliberate delay" which could distract new claimants from looking for work and drive them into the hands of payday loan firms.
Children educated at private school are likely to earn almost £200,000 more over the course of their career than their counterparts in the state system, new research suggests.
A study by the Social Market Foundation found that between the ages of 26 and 42 a privately educated person will earn approximately £193,700 more on average than someone who went to state school.
The difference means an average private school pupil will earn 43% more than their state school peers by the age of 34, although this falls slightly to 34% by the aged of 42.
A fall in the number of people unemployed is welcome, but people are now "worse off than when David Cameron came to office," says Shadow work and pensions secretary Rachel Reeves.
The comments come as the Office for National Statistics released its latest figures on UK unemployment numbers.
While this fall in overall unemployment is welcome, working people are over £1,600 a year worse off than when David Cameron came to office and pay has fallen behind inflation.
Thousands of people who work hard are struggling to make ends meet because of the Government's failure to tackle the cost-of-living crisis and make work pay.
Despite climbing figures in those in employment "workers are still not getting pay rises" says the general secretary of the Trade Union Council, Frances O'Grady.
He said: "Pay packets have nosedived since the Government prematurely declared an end to Britain's cost-of-living crisis last month.
"It's great that more people are joining the workforce but hugely worrying that workers are still not getting the decent pay rises they need to get by."
The comments come as the Office for National Statistics released its latest figures on UK employment numbers.
Employment minister Esther McVey has welcomed the latest figures on employment by the Office for National Statistics:
As we build a stronger economy, businesses up and down the country are feeling increasingly confident about creating jobs
Many thousands more people are in work every day - ensuring a better future for them, their families, and for the country as a whole.
Unemployment numbers have fallen by 347,000 from a year ago, but those still out of work is estimated at "around 500,000 higher" than before the financial crisis.
ITV News Business Editor Joel Hills reports:
Number of people employed in public sector (5.4m) has fallen by 280,000 in last year. Number employed in private sector up 1m to 25.1m.
2.16 million people are unemployed in UK. Down 347,000 on a year ago but around 500,000 higher than before financial crisis began.
Unemployment numbers fell by 161,000 between February and April to 2.16 million, official figures by the Office for National Statistics showed today.
Prime Minister David Cameron has tweeted that more people will have a "brighter future" after employment numbers were released by the Office for National Statistics:
A record rise in employment for last 3 months. 5500 more people in work each day. All with the security of a pay packet and brighter future.
Today we reached a major milestone in our #LongTermEconomicPlan: 2 million new private sector jobs since 2010. More security for people.
The average earnings for employees has increased by 0.7% in the year to April, meaning the growth of workers pay has slowed 1.7% in the previous month, the Office for National Statistics have said.
This slowdown in total pay was largely accounted for by bonuses, which fell sharply in recent months as tax changes were introduced.