The fresh cases include a Delhi Police personnel, a SpiceJet passenger and a Delhi Transport Corporation (DTC) employee, they said.
While three cases were reported from Kangra district, two were detected from Mandi district, Special Secretary (Health) Nipun Jindal said.
A 22-year-old woman from Bhaniara village in Shahpur in Kangra, who arrived on a SpiceJet flight from Delhi on May 26, tested positive for COVID-19, an official said.
A student, she was asymptomatic, he added.
A 56-year-old Delhi Police personnel also tested positive for the novel coronavirus, the official said.
A resident of Sunehar, he returned from Delhi in a car on May 27 and was asymptomatic as well, the official added.
Both of them are being shifted to the Panchayati Raj Training Institute (PRTI) in Baijnath, he said.
A 57-year-old ex-serviceman from Bairghatta in Dheera also tested positive, the official said, adding he returned from Delhi on May 30.
He works in the DTC and was in home quarantine since his arrival, the official said.
Having co-morbidity, the man is being shifted to the Dedicated COVID Health Centre (DCHC) at the zonal hospital in Dharamshala, he added.
In Mandi, two men, aged 23 and 31 years, who returned from Mumbai, tested positive for COVID-19, a district official said.
They are from Ladhbhadol and Paddar blocks and were institutionally quarantined at Jogindernagar, he added.
The number of coronavirus cases in the state has risen to 346. The active cases are 212, while 123 patients have recovered. Six have died of the infection, the officials said.
Hamirpur has the highest number of active cases in the state at 76, followed by 57 in Kangra, 18 each in Una and Solan, 13 in Chamba, 11 in Bilaspur, nine in Mandi, seven in Shimla, two in Sirmaur and one in Kullu.
On Tuesday, six patients -- five in Hamirpur and one in Una -- recovered from coronavirus, Jindal said. DJI AQS AQS