NSW Premier Gladys Berejiklian has again defended her state’s approach to the coronavirus pandemic, after five more community cases were reported on Tuesday.

“Anyone who thinks we’re going to eliminate or eradicate this disease, unfortunately doesn’t appreciate what the pandemic means,” she said.

The five local cases in NSW on Tuesday included two initially reported on Monday.

They are a man in his 40s who went to a Sydney hospital emergency department on Saturday night, and his partner. NSW Health is still trying to trace the origins of their infections, as Ms Berejiklian warned the coronavirus was still “bumbling along in the community”.

There were also two more cases on Sydney’s northern beaches, whose source is yet to be found, and another linked to the Berala cluster. NSW had 11 more infections in returned Australians in hotel quarantine.

• Cleaner’s husband ‘infectious’ before quarantine
• Victoria’s sixth ‘doughnut day’ as permit system begins

Ms Berejiklian said zero community transmission remained the national goal.

On Monday, Western Australian Premier Mark McGowan urged NSW to do more to “crush and kill” the virus.

NSW should aim to eliminate “the virus from Sydney” so all of Australia “could rest a lot easier”.

“There’s five states and two territories doing one thing, and one state doing something different. I go with the majority,” he said.

WA has kept its interior border closed for much of the pandemic and in recent weeks has rapidly re-implemented hard border arrangements for NSW, Victoria and Queensland. It has previously required other states to go 28 days with no COVID-19 community transmission before reopening its border.

“The idea that somehow it’s better to have the virus and then just manage it, I don’t think is the correct approach,” Mr McGowan said on Monday.

But Ms Berejiklian said Mr McGowan should reacquaint himself with national cabinet’s COVID-19 suppression strategy.

She reminded him Australia’s goal was not elimination but zero community transmission – particularly while overseas Australians continue to return home.

“Because we have confidence in our health system and health team, we’re able to make decisions which perhaps other state governments aren’t prepared to make,” she said on Tuesday.

“I don’t want a situation in NSW that exists in other states where there’s a lack of certainty, things are done very quickly without perhaps the same kind of consideration we give in NSW.”

With the exception of Victoria at the height of its second wave, NSW has kept its interstate borders open throughout the pandemic.

“Every state might have a different way of getting to zero community transmission and that’s a matter for them,” Ms Berejiklian said.

“I don’t believe keeping your borders closed and inflicting pain and suffering on thousands of people is the way to do that, but that’s just the NSW strategy.”

NSW authorities are, however, again concerned about testing levels across the state. Tuesday’s figures came from fewer than 15,000 tests.

“We really need to have higher testing levels if we are to combat the rumblings that are still going on and we know that it takes some time to completely get to the target of zero community transmission,” Ms Berejiklian said.

More coronavirus-affected venues in western Sydney and the northern beaches were identified on Monday night.

• See a full list of NSW venues of concern here

Authorities issued a close-contact alert for those at Blacktown Workers Sports Club’s Grange buffet restaurant at lunch time on January 3 and 10.

The club closed as a precaution on Monday for a precautionary deep clean.

Further alerts were issued for shoppers in Warriewood Square on the northern beaches for dates and times from December 31-January 8.

A pool shop in Brookvale, a Warriewood pharmacy, a post office in Hurlstone Park and a patisserie in Ashfield have also been added to the list of hotspots.

NSW has one COVID-19 patient in intensive care.

Elsewhere, the ACT has lifted travel restrictions for the Central Coast, Wollongong and some parts of greater Sydney.

ACT residents quarantining at home after previously visiting those regions have also been allowed to leave quarantine. Restrictions on areas such as Sydney’s northern beaches, inner-west and Parramatta remain.

-with AAP