Dan Du Preez, Ox Nche, Bongi Mbonambi, Scarra Ntubeni and Makazole Mapimpi have been forced into self-isolation alongside their captain and three members of team management.
"With the entire squad and management team confined to their rooms since Monday, the possibility of transmission through close contact has been mitigated," an SA Rugby statement read.
More than 20 members of the Springboks' squad have returned positive tests in the build-up to the three-match series, which is scheduled to begin on 24 July.
That number includes coach Jacques Nienaber, who is unable to work with his players as he continues to self-isolate.
Instead, South Africa's director of rugby Rassie Erasmus is taking charge of training sessions for the remaining members of the squad.
"We are delighted to be able to return to the field and resume our preparations for the Lions series,." Nienaber said.
"It has been a challenging week with the Test against Georgia on Friday night cancelled and the entire squad self-isolating for a few days as a preventative measure, so the players cannot wait to get back on the park.
"The Test against Georgia was important for us with an eye on preparing to face the Lions, but these are extraordinary times and we have to adapt as a team. I have to commend the players and management for that.
"We are a tight-knit coaching team and everyone takes responsibility in their respective roles. It is also great to have Rassie steering the ship while I am away.
"He has been part of the system for several years now and he guided most of these players to the World Cup title in 2019, so the team is in great hands."