The identities have not been confirmed by police, but upset neighbours told reporters at the scene a couple with three young girls - aged 3 and 18-month-old twins - lived at the address.
Coode Street resident Richard Fairbrother, who lives next door to the house where the bodies were found, said he last saw the family more than a week previously, as he had been away.
A man in his 20s turned himself to a regional police station on Sunday, ahead of police going to the home where they discovered the bodies around midday.
"The man is now in custody and assisting police with their inquiries".
Specialist forensic police are expected to continue a meticulous examination of the crime scene on Monday.
"There are no ongoing concerns for public safety as a result of this incident", they said.
"It's just horrific on every level".
'This is a tragic event and will have an impact on family and friends, the community, and the emergency services who first responded to the tragic scene.
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"She was such a handsome person and such a go getter and hard worker", she said. No further information was provided on the victims and the man in custody.
Police at the scene in Bedford, WA.
Forensic police officers inspect a property in Bedford, Perth after five bodies were discovered at the home.
Steel added the investigation was still at a "very early stage" and officers were still working to determine the timeline of what happened, ABC News reported.
"Just a normal family, you would never imagine anything like that happening", he said.
"It's always been so calm and peaceful". "No charges have been laid at this time".
In July, a 19-year-old man was charged with the murders of two children and their mother in another Perth suburb, Ellenbrook.
Ms Cambos revealed to Perth Now that the family's father ran a lawnmowing and landscaping business and she had not seen his work ute outside the premises for some days.