A 28-year-old man has been arrested in Anglesey on suspicion of terrorism offences.
Officers from Counter Terrorism Policing North East also arrested a 29-year-old man, a 30-year-old man and a 28-year-old woman in Keighley, West Yorkshire, on Saturday morning on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under Section 41 of the Terrorism Act 2000.
A 16-year-old boy was arrested in Swindon, Wiltshire, on Saturday morning on suspicion of the same offence.
All five have been taken to a police station in West Yorkshire for questioning, Counter Terrorism Policing North East said.
A number of properties are currently being searched in connection with the arrests which form part of an ongoing investigation into right-wing terrorism.
The statement added: "We recognise that local people may have concerns as a result of this activity.
"We would like to reassure them that these arrests are pre-planned and intelligence-led and there is not believed to be any immediate risk to the local community.
"We are grateful for the understanding, patience and support of local residents while these inquiries continue."