The jury heard evidence of how his former housemate had asked Moore to keep an ear out for the children while she was gone briefly.
On her return she found him lying on the couch next to her baby naked from the waist down.
Today Justice Pheroze Jagose sentenced the man to preventive detention with a minimum non-parole period of five years.
It means Moore will have to show he is no longer a risk to the community before he can be released from prison.
Justice Jagose described Moore's pattern of reoffending as forming and misusing adult relationships to gain access to vulnerable children.
"After observing the 30-year span of your sexual offending against five different children and your then partner I am satisfied you are likely to re-offend."
Justice Jagose said Moore was given an extended supervision order after being released from prison for other sexual offending.
The purpose of the supervision was for Moore to be monitored so that he didn't have contact with any other children.
But Moore breached the order at least 22 times, being recalled to prison on some occasions.
During one breach, Moore was caught talking to children at a playground. He is reported to have told authorities the children were being "sexually provocative".
In 2020, he cut off his bracelet and went on the run, eventually ending up living with the woman and her three children.
His lawyer, Susan Gray, told the court that Moore had previously been successful in rehabilitation for his sexual offending.
She said preventive detention would be mentally crushing for him and there will be no urgency to direct him to the services he needs.
"He works well with structures, relearning, and gaining insight.
"Moore has had a horrific childhood and was damaged considerably by it. Throughout his life, he has come in contact regularly with the criminal justice system.
"He has never had a job in his life and his background has jolted him from living a normal life."
Gray also mentioned that Moore expressed his remorse for the offending.
But Crown prosecutor Jacob Barry said this was a man who had seriously offended over a period of 30 years.
"Moore has a serious history of sexual offending and serious drug and alcohol abuse. He has received warnings in the past and will have little support when he gets back into the community.
"He cut his bracelet off and went on to sexually offend an infant."
Berry said it must have been apparent to him the potential consequences he could have faced.
"He has received warnings in the past, preventative detention is the appropriate sentence."
Justice Jagose said Moore's 10 past convictions of sexually violating young children and women meant that imposing a sentence of preventive detention was warranted.
"Your age at nearly 50 does not reduce your risk," he said.
Where to get help:
If it's an emergency and you feel that you or someone else is at risk, call 111.
If you've ever experienced sexual assault or abuse and need to talk to someone, contact Safe to Talk confidentially, any time 24/7: • Call 0800 044 334 • Text 4334 • Email support@safetotalk.nz • For more info or to web chat visit safetotalk.nz Alternatively contact your local police station - click here for a list.
If you have been sexually assaulted, remember it's not your fault.
If you have concerns or suspicions about someone who may be trading in or producing child sexual abuse images or videos, contact Customs confidentially on 0800 WE PROTECT (0800 937 768) or Crimestoppers anonymously on 0800 555 111.
If you are or know of, someone who is at risk or being abused, contact the police immediately.
