Four of the boys - aged six, four, three, and two - are in emergency care with foster parents. The youngest, aged just six months old, is with his father.
The father alerted police and social services when he discovered that the six-month- old was suffering severe nappy rash during an access visit to a house in the Middleton area of the city on Sunday.
Police were still searching for the mother of the children, who ran away when social workers called at their home.
The father applied for custody of the other children at a private hearing at Leeds County Court but the case was deferred until next week for a full social inquiry report to be prepared.
The latest incident comes just over a week after three young children were found living alone at home in the Little London area of Leeds by carol singers on Christmas Eve. They had been left with just a tin of beans and sausages to eat over the Christmas period and social workers found there was only 11 minutes of electricity left to provide heating and lighting for them.
Their father is due to appear in court latest this month facing charges under the Children and Young Person's Act.
On Christmas Day a nine- year-old girl was found alone in her house in the Scott Hall area of the city after her father had gone out drinking.
Michael Simmons, Leeds social services chairman, said the children in the latest incident were living in appalling conditions. 'The house was in a filthy state. It was basically a toilet,' he said. 'There was excrement everywhere and the children were walking in it.'
After they were removed from the house the children were given warm clothing, fed and bathed - possibly for the first time in weeks.
Mr Simmons said the children had been on the social services register and were attached to social workers, and added that there was a 'steady stream' of families with children found in this condition.
Police confirmed that two children killed in a house fire at Hayes, west London, last night were with their mother at the time. At first it was feared the girl, aged four, and her brother, three, had been left alone. Their mother was being treated for shock.Reuse content