The arrests occurred in Manchester in the north-west, in Peterborough in eastern England and in London.
Some of the suspects, aged between 19 and 23, are accused of preparing a terrorist act. All five are in police custody, Dpa reports.
“The arrests were part of a pre-planned operation and it is not believed there will be any imminent threat to the public in relation to this,” the police statement said.
According to police, the arrests are not related to the knife attack near London Bridge that left two people dead in late November or the upcoming New Year celebrations in the British capital.