It has been confirmed that two people in Oxfordshire and three people in Wiltshire have been diagnosed with the coronavirus.
It comes as the number of people who have tested positive in the UK reached 115, 17 of which are in the South East.
Oxfordshire County Council said the two new cases are not linked to one another and are associated with foreign travel.
Meanwhile, the three people diagnosed in Wiltshire are known to each other and are linked following a trip to Northern Italy. All three people are self-isolating at home.
Public Health England is getting in touch with people who have had close contact with the five confirmed cases of Covid-19.
It said: "Close contacts will be given health advice about symptoms and emergency contact details to use if they become unwell in the 14 days after contact with the confirmed case. This tried and tested method will ensure we are able to minimise any risk to them and the wider public.”
The Director of Public Health at Oxfordshire County Council, Ansaf Azhar, said the risk to the general public "remains low" and the council is "working with health colleagues to do everything we can to stop the virus spreading and ensure the people of Oxfordshire are protected".
The public is being urged to follow national Government guidance to prevent further spread of the illness and limit the numbers affected.
As of 9am on 5 March 2020, 18,083 people have been tested in the UK, of which 17,968 were confirmed negative and 115 were confirmed as positive.
Current evidence indicates that most cases appear to be mild, with patients experiencing flu-like symptoms.
What are the symptoms of Covid-19?
- a cough
- a high temperature
- shortness of breath
Older residents or those with weakened immune systems or long-term conditions may experience more severe symptoms.