The shooting occurred in an apartment in the Howard Houses public housing complex on Glenmore Avenue just before midnight.
Residents of a sixth-floor apartment had organized a party and put the word out on Facebook, said Tony Herbert, a community activist who said he had spoken to some of the guests and those injured.
Some people who'd had previous conflicts with the party crowd showed up outside the Glenmore Avenue building, and bullets flew in the lobby as the teenage victims tried to run back inside, Herbert said.
Two 18-year olds and three 16-year olds were wounded in the legs. Authorities say four of the five have arrest records.
A 17-year old girl was also pistol whipped during the incident.
The wounded were taken to Brookdale University Hospital and other nearby hospitals.
The suspect, a man in dark clothes, fled the scene. So far police have not not recovered a weapon, and they say the victims are not cooperating.
Herbert planned to gather with other community advocates Tuesday to call for calm.
"Our concern is that the attitude, with these young people, is that this may now be an occasion for retaliation," he said. "We're going to try to keep the peace."
The Associated Press contributed to this report.