South Australian authorities say there are now 20 confirmed cases linked to the Parafield coronavirus cluster and another 14 suspected cases.

Chief Public Health Officer Nicola Spurrier says the suspected cases are considered at high-risk of becoming a case, have symptoms and are close contacts of the confirmed cases.

They are either waiting for test results or have had a negative test result but are being tested again.

In all, South Australia has recorded five new cases today — one an aged care worker and three family members of a security guard who worked at a medi-hotel.

Professor Spurrier said the fifth new case — the 20th overall — had just been confirmed and the person was being interviewed to determine the source.

About 4,000 close contacts are in quarantine.

Premier Steven Marshall told State Parliament this afternoon there were "in excess of 5,300 tests conducted yesterday" and another 6,000 were expected to be done today.

"This is nothing short of sensational and would be a record for South Australia, so my heartfelt thanks to everyone in South Australia who has heeded the call to get tested," he said.

Hotel confirmed as source

Mr Marshall said the virus was transferred to a cleaner at the Peppers Waymouth medi-hotel "via a surface" and that they believe she infected two security guards but none were symptomatic.

He said he did not believe there had been a breach of the state's hotel quarantine system, but SA Health would conduct a "fulsome" review once the threat of the Parafield cluster was over.

"We all know that the incubation period for this disease can be up to 14 days so we still do have an anxious wait to see what the true situation is in South Australia but there is more and more data coming in all the time," he said.

Dr Spurrier confirmed genomic testing had determined the virus strain had come from a traveller staying at the Waymouth Street hotel.

She said the person arrived in Australia on November 2 and was tested on November 3.

The woman who worked at the hotel was the daughter of the 80-year-old who attended the Lyell McEwin Hospital on Friday night and sparked the alert.

Five schools have now closed because of connections with the northern suburbs cluster — Roma Mitchell College in Gepps Cross, Mawson Lakes School and Preschool, Thomas More College in Salisbury Downs, Holy Family Catholic School in Parafield Gardens and Mount Carmel College at Rosewater.

SA Health has released a list of dozens of locations across Adelaide where people could have become infected.

Authorities have urged people to get tested if they have developed symptoms after visiting those locations.

New coronavirus restrictions came into force at midnight, including limits on gatherings in homes and licensed venues and a temporary ban on community sport.