A five-year-old boy died days after cutting his foot on rubbish in his family's filth-ridden Melbourne home after his parents failed to take him to a doctor, according to court documents.

The boy received a three-centimetre cut to his big toe when he stepped on an open can of cat food that had been discarded in the house and was piled among junk, food scraps and faeces that filled every room of the house, in Melbourne's north-western suburbs, the documents say.

On August 1, 2012, several days after the injury, he could not be revived by ambulance paramedics after the boy's mother had rushed him to an ambulance branch office. One paramedic said in a statement to police that the boy had grey, mottled skin when he was brought to them and that he had a filthy bandage wrapped around his foot.

According to court documents, the boy had a headache and sore neck the night before he died, and was heard by his older brother calling for help and looking ''very, very, very sick''.