Police say a 67-year-old man went into a neighbour's unit on Saturday evening, fatally shooting four people as they ate dinner.

They say the suspect then went to a unit on the floor above and shot another woman, who died of her injuries on Sunday.

The suspected gunman had not yet been identified or charged as of Sunday afternoon. He was taken into custody shortly after the shooting on the city's Northwest Side.

First Deputy Supterintendent Antony Riccio says the man had a history of issues with his neighbours but investigators "don't know what set him off".

Riccio says it's not clear how he was able to enter the apartments but there was no sign of forced entry.

Australian Associated Press