An update was given by president Edouard Fritch, who told the public broadcaster that among the five is education minister Christelle Lehartel.
She has been in isolation for a week.
Mr Fritch also warned that a curfew may be declared because too many people flout the restrictions put in place at the weekend in an effort to curb the spread of the disease.
There had been cases of people being out without the required attestation allowing their movement, he said.
There had also been instances of people meeting up in defiance of existing orders.
Mr Fritch said further restrictions on the sale of alcohol were being considered.
Public servants employed by the French Polynesian government have been ordered to stay home as part of special leave.