Among them is alleged terrorism fundraiser Babar Ahmad, 37, who has been held without trial since 2004
They also include radical cleric Abu Hamza, who lodged an appeal on Monday. A sixth man has not yet appealed.
A panel of judges will decide in September whether the cases should go to the Grand Chamber. In the meantime, none of the suspects can be extradited.
The other cases involve Mr Ahmad’s co-accused Syed Talha Ahsan, and Adel Abdul Bary and Khaled al-Fawwaz, who are accused of being key aides to Osama bin Laden in London.
The sixth suspect, Haroon Aswat, has not lodged an appeal because the ECHR requested further legal submissions on his case.
On Monday, Abu Hamza, 54, appealed to the ECHR 24 hours before the deadline expired – further delaying his extradition.
The terror charges on the indictment include hostage-taking in Yemen in 1998.
In April, the European Court of Human Rights backed the extradition of the men from the UK to the US.
The Strasbourg court held that their human rights would not be violated by the prospect of life sentences and solitary confinement in a US “supermax” prison.
The court’s decision was seen as one of its most important since 9/11. A ruling that human rights are observed in US maximum security prisons is expected to make it easier for the UK to send suspects to America.
Following news of Abu Hamza’s appeal on Monday, the Home Office said it had welcomed the court’s original judgement, but accepted that it would not be final in any of the cases until the appeal was decided.
All five men would remain in extradition custody, a spokesman added.
Abu Hamza is also accused by the US of planning to establish a training camp in Bly, Oregon. There are further allegations that he plotted to provide material support to terrorists in Afghanistan and provided goods and services to the Taliban.
He was first arrested at the request of the US in May 2004 – but the extradition was halted after he was jailed at the Old Bailey for incitement offences relating to his sermons in London.