Unemployment was 28,000 lower in the three months to January at 1.68 million, the sixth consecutive quarterly fall.
The number of people on the claimant count, including those on Jobseeker's Allowance, was cut by 18,000 last month to 716,700, the lowest since 1975.
Employment has reached a record high of 31.4 million after an increase of 116,000 in the latest quarter. The number of people in work has now risen by almost half a million over the past year.
Job vacancies are up by 10,000 to 768,000, the Office for National Statistics (ONS) reported.
Average earnings increased by 2.1% in the year to January, up by 0.2% on the previous month.
ONS statistician Nick Palmer said: "Once again the latest quarterly figures show continuing high employment levels but no significant pick-up in earnings growth."
Public sector employment increased by 3,000 to 5.3 million, largely due to a rise in the number of NHS staff. Local government employment fell to a record low of 2.2 million.
The number of people employed in private firms has increased by over half a million over the past year to 26 million.
Other figures revealed a 177,000 increase in part-time workers to almost 8.5 million in the past year.
The number of people classed as economically inactive, including those on long-term sick leave, looking after a relative or who have given up looking for work, fell by 40,000 to just under 8.9 million, a near-record low rate of 21.8%.
Wales First Minister Carwyn Jones said: "Today's figures show a sharp decline in the rate of unemployment in Wales and employment rate at an historic record high.
"The labour market in Wales continues to outperform the UK as a whole and the Welsh economy is going from strength to strength."
Employment Minister Priti Patel said: "This is another strong set of figures showing private sector employment at the highest since records began, wages rising and a near record number of job vacancies available in the UK economy.
"With unemployment now standing at 5.1% - half the eurozone average - it's clear that we are delivering on our promise to support people to get on in life, and create greater economic security for all."