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. The shooter's 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.