The five, all aged around 20, began their sentence on Wednesday afternoon at "prison six", a military jail near the northern Israeli town of Atlit.
They were sentenced on Sunday by a military court in Jaffa, near Tel Aviv, after the judges overruled as "politically motivated" their refusal to serve in the army on grounds of conscience.
Matan Kaminer, Noam Bahat, Shimri Tsameret, Adam Maor and Hagai Matar have already been on remand for a year, serving three months behind bars and another nine months in an open prison.
Unlike the others in Israel's growing refusenik movement, the five refused to serve in the Israeli Defence Forces (IDF) in any sphere, not just in the occupied Palestinian territories, on grounds of conscience.
By contrast, the majority of other refuseniks limit their "refusal" to service in the West Bank and Gaza.
But the prosecution rejected their position as "selective objection" rather than "conscientious objection." It said their refusal was not about serving in any army, but only in one specific army - the IDF - on account of its activities in the territories.
This is one of the first instances of soldiers being court martialled for conscientious objection since 1979, Yesh Gvul spokesman Yishai Menuchin told AFP.
Normally, anyone refusing to serve is judged by a disciplinary judge who hands out sentences of between 28 to 35 days, but a court martial is authorised to hand out much longer sentences, he said.
The first time an individual was court martialled in more than 20 years was in November, when Yoni Ben Artzi, the nephew of Finance Minister Benjamin Netanyahu, was refused the status of conscientious objector, he said.
The five refused to serve in IDF
in any sphere
Ben Artzi has not yet been sentenced.
At their sentencing, the court recommended that following the year, the army consider discharging them, but the military prosecutor said the army would demand that they be mobilised again, Yesh Gvul said.
"We did not expect anything else from the tribunal of an army which occupies and oppresses a whole people and from a regime which has forgotten the meaning of democracy," Matar told AFP following the ruling on Sunday.
The five are among the signatories of a letter sent by over 200 secondary school students to Israeli Prime Minister Ariel Sharon in September 2002 in which they said they would refuse to serve in an "army of occupation."