The students, in their 20s and from the U.S. state of Virginia, were detained in December in the central Pakistani town of Sargodha, 190 km (120 miles) southeast of the capital.
They have not been formally charged, but could face lengthy prison terms if found guilty.
The case of the Americans has underscored global security dangers posed by the Internet as militants use cyberspace to evade tighter international security measures and plot holy war.
A defense lawyer for the five, who appeared in an anti-terrorism court in Sargodha, requested bail, saying allegations against them were vague.
No substantial evidence is available to show their guilt, the lawyer, Mohammad Shahid Kamal Khan, told reporters.
It's a violation of their legal and fundamental rights to keep them in confinement, he said, adding he expected the court to decide on the bail request on Wednesday.
The five told the court earlier they only wanted to provide fellow Muslims in Afghanistan with medical and financial help.
They have accused the U.S. Federal Bureau of Investigation and Pakistani police of torturing them and trying to frame them.
Pakistani authorities have denied the accusations of mistreatment, which the five repeated on Tuesday, saying authorities were trying to force then back to the United States on phony charges.
We have been threatened to be tortured again if we continued to speak out the truth, one of the five wrote on a piece of tissue paper dropped from a police van as they arrived at court.
Khalid Farooq, the father of one of the accused, said they were innocent. There is no question about that, he said.
Two of the five are of Pakistani origin, one of Egyptian, one of Yemeni and one of Eritrean origin. They were arrested days after arriving in Pakistan.
Police have said emails showed they contacted Pakistani militants who had planned to use them for attacks in Pakistan, a front-line state in the U.S.-led war against militancy.
Pakistan is struggling against al Qaeda-linked militants and is under pressure from Washington to help stabilize neighboring Afghanistan, where a Taliban insurgency is raging.
The United States says Pakistan must crack down harder on militants who cross into Afghanistan and attack U.S.-led troops.
(Writing by Augustine Anthony; Editing by Robert Birsel and Ron Popeski)