Officers from the North West Counter Terrorism Unit arrested the five men at addresses the north west in a co-ordinated operation starting at 4am, Greater Manchester Police said.
Three properties in Manchester and one in Bolton were being searched, a force spokesman said. The addresses searched were in Stockport Road, Levenshulme; Victoria Road, Longsight; Bowdon Avenue, Fallowfield, and Willows Lane, Deane, Bolton.
The spokesman said: "People living in nearby communities will see a high profile police presence during the day and will be able to discuss issues with local officers.
"This was a low-key operation and no armed officers were involved.
"There is no further information available at this time."
Police sources said there was no imminent terrorist danger to the Greater Manchester area and the arrests were related to an alleged overseas threa