The cases were diagnosed from more than 160,000 tests in the 24 hours to 8pm on Wednesday and represent an increase of 1952 from Tuesday.
The figure is just shy of the 5725 cases reported across Australia on Wednesday.
One death was also reported on Thursday.
The number of people in hospital has climbed to 347, up 45, with 45 in ICU.
NSW Health says most patients are unvaccinated.
The dramatic spike in cases, which comes on two days before Christmas, increases the pressure on the NSW government to reintroduce some restrictions.
Minister for Customer Service and Digital Victor Dominello on Thursday announced the government had changed its mind on mandatory check-ins to venues across the state.
"Given the increasing Omicron numbers we'll revert back to our pre-15 Dec check-in settings," he tweeted.
Check-ins will be mandatory again at supermarkets, shops and hospitality venues.
But Premier Dominic Perrottet is still resisting bringing back mask mandates at indoor venues, despite NSW Health urging everyone to wear them in high-risk settings.
The government is however considering providing free rapid antigen tests via mail, as testing clinics are overwhelmed and wait times - both for the test and the result - blow out.
Mr Perrottet emerged from a national cabinet meeting on Wednesday to flag a plan to provide residents with the rapid tests, which are in short supply and expensive.
"Providing rapid antigen testing kits for those who want to do the right thing will help take the pressure of our testing clinics while giving people confidence to get on with their lives," he said on Wednesday.
"This will also help people monitor their symptoms and go about their daily activities in a responsible manner helping protect themselves, their families and the community."
The need to relieve pressure on COVID-19 testing sites across the state is becoming more urgent with just two days until Christmas, after days of long queues at the facilities.
People wanting to travel interstate or get the all-clear to attend Christmas celebrations are waiting hours to get a PCR test and around 72 hours to get a result.
After NSW Health Minister Brad Hazzard on Tuesday blamed "tourism testing" for long queues at testing sites, national cabinet on Wednesday asked a national medical expert panel for advice on whether negative tests should continue to be required for interstate travel.
Meanwhile, tens of thousands of people in NSW are facing Christmas in isolation as the Omicron variant of COVID-19 continues to run rampant.
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