It was the lowest jobless rate since the three-month period to January 2006, according to the Office for National Statistics (ONS).
The number of people out of work fell by 110,000 to 1.71 million between August and October, reports The BBC.
There were 31.3 million people in work, 505,000 more than for a year earlier.
Joblessness had been expected to remain at 5.3 per cent, where it was a month ago, according to a poll of economists by news agency Reuters.
The figures also show EU citizens working in the UK increased by 324,000 to 2.02 million, whereas workers who were neither EU nationals or Britons were “little changed” at 1.20 million.
The jobless rate a year ago was 6 per cent.
The pay of workers grew at its slowest rate since the January to March period, in spite of the unemployment dip.
Total pay grew 2.4 per cent.
“Earnings continue to grow in real terms, although at a slower rate than we have seen in recent months,” ONS statistician David Freeman said.
Bank of England Governor Mark Carney has said he would like to see earnings growth above 3% a year before he would increase interest rates. A rate decision is expected from the US central bank, the Federal Reserve, later on Wednesday.
“It is a foregone conclusion that the Fed is going to raise rates,” said Kully Samra, a managing director at US investment manager Charles Schwab.
Vacancies of 747,000 in the UK jobs market have not been higher since data began in 2001, said the ONS.
The number of hours worked per week topped one billion for the first time, the ONS said. This was a consequence of more people in work, “as average weekly hours per person are fairly stable,” said Mr Freeman of the ONS.