(CNN) -- Endurance swimmer Diana Nyad reached the shores of Key West on Monday afternoon, becoming the first person to swim Cuba to Florida without a shark cage.
This was the 64-year-old's fifth attempt since 1978.
Dozens of onlookers -- some in kayaks and boats, others wading in the water or standing on shore -- cheered her on as she wrapped up the swim.
As the team called her around dawn for her first feeding since midnight, she took longer than normal to reach the support boat, the report said.
Though she slurred her speech, the words were understandable. Before resuming her swim-crawl to Key West, her team applied a "sting stopper" substance to her forehead and cheeks in the hopes of warding off jellyfish stings.
"Don't get it on my nose or eyes," she said, according to her website.
Jellyfish stings have helped thwart her attempts before, so divers are swimming ahead of her, collecting jellyfish and moving them out of Nyad's path.
When instructed Monday morning to follow the path that's been cleared for her, she flashed her sense of humor, replying: "I've never been able to follow it in my life," according to the website.
Nyad's home stretch followed an overnight in which she became so cold, the team didn't stop her for feeding until first light "in the hopes that swimming would keep her warm," the website said.
Every stroke she swims puts her deeper into record territory. On Sunday night she broke Penny Palfrey's record for the farthest anyone has managed on the trek without a shark cage.
In 1997, Australian Susie Maroney completed the swim from within a shark cage. She was 22 at the time.
Nyad's website reported the leaders of her five-boat support team were planning her final route into Key West, taking into account tides, currents, shipping lanes, reefs and "swarms of jellyfish."
"Diana has stopped numerous times to tread water trying to restore herself," Nyad's navigator, John Bartlett, said in a website post at 5 a.m., 44 hours into the swim.
Nyad has been wearing a jellyfish protection suit, and also has available a special mask to prevent jellyfish stings to her tongue -- a key factor in her failed attempt in August 2012.
Thunderstorms also helped thwart her last year.
The weather this weekend was much better until 11 p.m. Sunday, when the support team reported winds rose suddenly and a thunderstorm appeared headed toward Nyad's path.
But just before 1 a.m. Monday, the team reported on Twitter: "Diana is swimming strong, everyone is safe, the winds are dying down, and we think we see the glow of Key West! "
Bartlett wrote on her website earlier that a favorable Gulf Stream had helped her achieve an average speed of 2.2 miles per hour.
Bartlett said currents will be "smaller but less predictable" as Nyad nears Florida.
Handler Bonnie Stoll wrote on the site Sunday that Nyad was in good spirits.
"The only concern is that she is throwing up everything she eats. She's quite nauseous from sea salt, but that's to be expected," said Stoll. "We're giving her enough calories and nutrition. We're just going to keep feeding her, and we hope that some of it is going down. She's not weak. Her stroke count hasn't changed."
Nyad set out from Havana at 8:59 a.m. Saturday with a crew of 35, including divers to watch for sharks.
The Los Angeles woman has said this is her final attempt. She said on her website that she wants to prove "it's never too late to chase your dream."
Track Diana Nyad's swim: http://www.diananyad.com/
CNN's Patrick Oppmann from Havana, Cuba, and Matt Sloane contributed to this report.
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