"Even if there was an interest, that interest is far outweighed by the interests of your children," she told the couple.
Judge Aitken said the children were the victims of their parents' crime and could be re-victimised and subjected to "taunting and teasing" in the school playground.
As well as the permanent suppression order, the pair are seeking a discharge without conviction.
The man's lawyer, Kyle Bendall said his client had attended 16 counselling sessions but had two more to do. He said the man was keen to have the matter dealt with.
Judge Aitken said she would sentence both defendants at the same time because their cases were linked.
She said there were "excellent reports" from both of their counsellors.
The pair are due to be sentenced next month.
The Herald has previously reported that surveillance footage shows the five children were left for about 45 minutes from 11am on Sunday, February 26.
They were found by a couple. The woman said at the time that the children were clearly distressed.
"I could see this little toddler up against the window screaming and banging," she told TVNZ's Close Up.
She said she could see a little boy trying to calm a baby.
"He was looking at me [shaking his head], 'No, no, no', and he had a cellphone in his hand."
Security guards worked with police to free them and they were put into the care of Child Youth and Family.
