The Prime Minister Manasseh Sogavare said all five cases involved passengers on a recent repatriation flight connecting through Auckland in New Zealand.
Sogavare said four of the people who tested positive were local footballers returning from the United Kingdom and the fifth person was a Korean national.
"All five new cases have been transferred to the national referral hospital isolation units. These five new cases bring the total number of cases from the flight from Auckland to nine. The total number of cases registered in Solomon Islands now is 13," said Manasseh Sogavare.
Meanwhile, Sogavare said although the first four people to test positive for Covid-19 in the country have now tested negative for the virus they will be closely monitored and will undergo further tests before being released.
The prime minister said daily health monitoring was continuing for all quarantined passengers.
"Swabbing and further tests are also underway as part of our testing protocols," he said.
Sogavare also sought to reassure the public that all cases had been contained within the isolation stations and the threat of community transmission remained low.