They are National Games bronze medalist Lau Chi-ming, Wong Cheuk-lee, Cheung Chu-ngan, Max Lau and Leung Man-him.
They competed at the Asian Championships this week and returned to Hong Kong on Thursday night.
The institute said 13 athletes, coaches and staff members who are considered to be their close contacts were sent into quarantine at Penny’s Bay.
The five athletes who tested positive are in hospital. Lau Chi-ming said he has a bit of a soar throat, but was otherwise feeling alright.
He said during the competition at Almaty, Kazakhstan, he saw many people flouting anti-epidemic rules and didn’t wear masks.
Spectators were also seen entering the venue where the final was held when only athletes were allowed, Lau told RTHK.