The five cases, aged 45 to 69, had visited Da Nang Hospital to take care of their relatives before they tested positive for the SARS-CoV-2 virus on July 30.
Four of the new cases live in Hoi An Ancient Town, a UNESCO-recognised World Heritage Site.
Quang Nam province has decided to impose a social distancing order on Hoi An, starting midnight July 31.
Inter-sectoral forces have cordoned off and disinfected residential areas where the patients live to prevent the virus from spreading in the community.
Local residents have been advised to stay indoors as much as possible, avoid gatherings in public places, and don face masks if they leave for daily necessities.
All tourist sites in Hoi An have been left deserted before the social distancing order takes effect.
Vietnam has confirmed 48 locally transmitted cases in six localities across the country since the first such case was detected in Da Nang five days ago.
Da Nang has now recorded 34 cases, topping the list, followed by Quang Nam (8), Hanoi (2), Ho Chi Minh City (2), Quang Ngai (1) and Dak Lak (1).
The Ministry of Health on July 30 decided to dispatch additional specialists to Da Nang to help the city deal with the outbreak.
As of 6pm July 30, as many as 464 coronavirus cases have been confirmed in Vietnam, with 369 of them having fully recovered from the disease. The remaining 95 patients are receiving treatment at healthcare facilities across the country.
No deaths have been reported so far, according to the Ministry of Health.