Police have released a photo of the suspect, who is described as a male in his late teens or early 20s wearing a black shirt and shorts. His motive is unclear.
The deaths took place inside Macy's department store at Cascade Mall in Burlington, near Seattle.
The FBI said there is no evidence that the shooting was linked to terrorism.
Police confirmed four women were killed inside Macy's. A man later died in hospital. They have not been identified.
Speaking at a news conference on Saturday morning, Lt Chris Cammock said security footage showed the suspect entered the mall without a weapon. Ten minutes later the video shows the suspect entering Macy's with a rifle.
Police arrived after the gunman got away and do not know which direction he took. They have asked community members to contact local law enforcement with any tips.
Burlington Mayor Steve Sexton said: "The city of Burlington has probably changed forever but I don't think our way of life needs to change."
He urged the community to come together in the midst of the crisis and support law enforcement in their efforts to track down the suspect.
Burlington is about 65 miles (105km) north of Seattle.
A manhunt is under way for a gunman who killed five people at a shopping centre in Washington state on Friday.