Bomb disposal officers were sent to Birmingham's Lee Bank area on Friday and nearby roads were closed and cordoned off.
The men, two aged 32 and 37 were arrested in Stoke-on-Trent and three others, aged 18, 24 and 28, were arrested in Birmingham.
Magistrates granted police a further seven days to question the men.
Detectives from the West Midlands Counter Terrorism Unit appeared before London's Westminster Magistrates' Court via video link on Saturday to submit their request for a warrant of further detention, a spokesman said.
The men were arrested on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.
Ch Supt Sue Southern, from West Midlands Police, said: "The arrests of the five men were intelligence led and our investigation continues at full pace."
A number of properties in the Stoke and Birmingham areas have been searched as part of the investigation.
The BBC understands the force was dealing with two suspect devices that were found at a business in Lee Bank on Friday.
Police have been given more time to question five men arrested on suspicion of terrorism offences.