The group – all in their 20s - were detained in the departure area of the port on Friday morning.
Officers now have until 8am next Friday, April 10, to charge, release or apply for another warrant of a further detention.
Police said the investigation was continuing and that the suspects - who are not a family group and were not accompanied by children - did not pose any immediate risk to public safety.
The men, are all aged between 25 and 26, are from Small Heath, Alum Rock, Acocks Green and Lozells, The woman is 28 and of no fixed address.