With American crew member Casey Smith already below deck because of a back injury, Puma was also without Tomas Johanson after the Finnish Olympic gold medallist hurt his shoulder when a huge wave hit the deck of the boat.
Three crew members, led by helmsman Jono Swain, consulted with medics back on land before popping Johanson's shoulder back into place as the boat neared the Southern Ocean.
"Johanson had been in a bunk writhing in pain but, thanks to the assistance of the doctors back on land, Jono just slowly popped his shoulder back in place," said skipper Ken Read of Newport, Rhode Island. "It was a Eureka moment and you saw his eyes open up. It was instantaneous relief."
Fourth overall, Puma was running second in the fifth leg as the boats attempted to use a fast moving weather system to speed them on toward Cape Horn.
Puma finished second in the fourth leg and was runner-up in the Auckland in-port race to revive its campaign after the boat lost its mast in the opening leg.
The American boat is 39 points behind overall leader Telefonica of Spain. But with 30 points available to the winner of each of the remaining five offshore legs, Pumas is still in the running.
All the boats are using the current light conditions to carry out repairs following brutal conditions in the first 48 hours of the fifth leg, which began on Sunday.
The Abu Dhabi entry was forced to return to Auckland for repairs on the first night, but was back within 300 nautical miles of the fleet by Wednesday.
The boats are due to reach Brazil about April 4.