Police have been searching for the five since February 12, when they arrested student union leader Kanhaiya Kumar for sedition over a rally at which anti-India slogans were shouted.
Protests in India over student leader's sedition arrest
The arrest raised fears over freedom of speech in the country's top universities.
Kumar, who like the other five is from New Delhi's prestigious Jawaharlal Nehru University (JNU), says he was not among those shouting the slogans.
He was beaten by right-wing nationalists when he appeared in court last week in an apparently orchestrated attack that has been condemned by rights activists and scholars around the world.
One of the five students, Anant Prakash Narayan, said he had gone underground because he feared "mob fury" but was ready to face justice.
"We are not scared of the police or the legal proceedings. We are ready to face everything because we have not done anything that is wrong," he told the NDTV news channel from the JNU campus.
Indian teachers strike to protest student's arrest
"We decided to come out in the open because the situation has cooled down now. We were scared of mob fury, not of anything else."
The students' reappearance has presented police with a dilemma because officially they need permission from the university's vice-chancellor to enter the campus.
Police vehicles were lined up outside the university on Monday, with the vice-chancellor locked in meetings to decide whether to allow them access.
Students have accused Prime Minister Narendra Modi's right-wing nationalist government of misusing the British-era sedition law to stifle dissent.
Modi has not directly commented on the row, but on Monday he addressed students at a major university in his northern constituency of Varanasi.
Last week, as students around the country marched against what they say is a clampdown on dissent, his government ordered all public universities to fly the national flag on campus.
The students were also protesting at the arrest of a former Delhi university professor for sedition earlier this month.
Indian opposition raises concerns with Modi over student protests
Both charges relate to events called to commemorate the 2013 hanging of Kashmiri separatist Afzal Guru over an attack on India's parliament.
On Monday Delhi's police chief B S Bassi, who has come under fire for his force's arrest and failure to protect Kumar, urged the five students to give themselves up.
"If they are innocent, they should present proof of their innocence," he said.
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