A 22-year-old man claiming to be the gunman handed himself to the nearby Ghyvelde police station at 5pm local time.
He told police he first killed a 29-year-old in the French town of Wormhout at about 3pm.
He then killed four others at the Loon-Plage refugee camp, he told police.
The four victims at the camp are understood to be two “security agents” and two migrants.
Sky News spoke with a witness who said the attacker pulled up in green vehicle, jumped out and fired around a dozen shots.
The gunman is thought to be a French national from Dunkirk and was carrying three more guns in his car, according to local media.
Milenkovic scored for the second week running as he struck in the 87th minute to cancel out Jhon Duran’s header for Villa.
Roared on by the City Ground crowd, Forest then claimed all three points in the third minute of stoppage time as substitute Elanga slotted a shot past goalkeeper Emi Martinez.
Forest moved a point above champions Manchester City, who host Manchester Untied on Sunday, into fourth spot with 28 points from 16 games while Villa, who were on course to go fourth themselves, stay sixth with 25.
After a totally forgettable opening half, the second period caught fire after a remarkable save by Martinez.
Forest’s Nicolas Dominguez could hardly believe his eyes as the Argentina World Cup winner showed amazing reflexes to somehow claw his close-range header off the line.
A minute later Villa’s first attempt at goal resulted in them taking the lead as Duran met John McGinn’s clipped cross with an instinctive header that flew past keeper Matz Sels.
It looked as though Forest’s luck was out when Chris Wood thought he had equalised but his effort was chalked off for the tightest of offside decisions after a lengthy VAR check.
Forest refused to be denied though and Milenkovic connected with a cross by Morgan Gibbs-White and this time Martinez was unable to keep the ball out of the net.
Elanga looked razor-sharp after coming off the bench and won it for Forest when he met a cut-back from Elliot Anderson
