Scotland Yard arrested a 51-year-old man, a woman aged 53 and three females aged 16, 17 and 19.
All five were arrested on suspicion of "possessing information likely to be useful to a person committing or preparing an act of terrorism" and remain in police custody in central London.
The man was also arrested on suspicion of possessing false identity documents.
Metropolitan Police said the 16-year-old girl had previously been arrested in July on suspicion of preparation of terrorism and had been bailed until September.
It has not been confirmed whether the case was linked to ISIS, which calls itself the Islamic State, or what the intended acts of terrorism were.