Story highlights Diana Nyad sits down with CNN Chief Medical Correspondent Dr. Sanjay Gupta

"You are never too old to chase your dreams," she says after 53-hour swim

Nyad becomes first person to swim from Cuba to Florida without shark cage

This was Nyad's fifth and final attempt to make 103-mile swim

"Find a way."

That's the mantra Diana Nyad said she had this year. And that's exactly what she did.

On Monday, Nyad became the first person to swim from Cuba to Florida without a protective cage, willing her way to a Key West beach just before 2 p.m. ET, nearly 53 hours after jumping into the ocean in Havana for her fifth try in 35 years.

Shortly after conquering the Straits of Florida, the 64-year-old endurance swimmer sat down with CNN Chief Medical Correspondent Dr. Sanjay Gupta.

"It's all authentic. It's a great story. You have a dream 35 years ago -- doesn't come to fruition, but you move on with life. But it's somewhere back there. Then you turn 60, and your mom just dies, and you're looking for something. And the dream comes waking out of your imagination," Nyad said.

The swim wasn't easy.

"With all the experience I have, especially in this ocean, I never knew I would suffer the way I did," she said. "For 49 hours the wind just blew like heck, and it was rough."

Photos: Photo: Diana Nyad's record setting swim Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Diana Nyad became the first person to swim from Cuba to Florida without a protective cage, reaching a Key West beach on Monday, September 2, nearly 53 hours after jumping into the ocean in Havana for her fifth try in 35 years. The 64-year-old endurance swimmer had a 35-person team to help clear her path of jellyfish and watch for sharks. Hide Caption 1 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad speaks during a press conference in Havana, Cuba, on Friday, August 30. Hide Caption 2 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad jumps into the water to begin her fifth attempt at crossing the Straits of Florida on Saturday, August 31. Hide Caption 3 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad waves after starting her journey without a shark protection device on August 31. Hide Caption 4 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad is escorted by kayakers two miles off the coast of Key West, Florida, on Monday, September 2. Hide Caption 5 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad talks with her crew on September 2. Hide Caption 6 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – People cheer as they await Nyad in Key West on September 2. Hide Caption 7 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad completes her swim from Cuba as fans cheer. Hide Caption 8 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad and her trainer Bonnie Stoll hug as Nyad walks ashore on September 2. Hide Caption 9 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – Nyad takes a drink after completing her swim from Cuba. Hide Caption 10 of 11 Photos: Photo: Diana Nyad's record setting swim Diana Nyad's record-setting swim – The journey was more than 100 miles from Havana to Key West and took Nyad 52 hours and 54 minutes. Hide Caption 11 of 11

Photos: Photos: Diana Nyad's long swim Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Diana Nyad swims along Florida's Gold Coast in July 1978. On her fifth attempt, Nyad, now 64, became the first person to swim the 103 miles from Cuba to Florida without a shark cage. The endurance swimmer achieved her lifelong ambition of conquering the Straits of Florida on Monday, September 2, after four earlier setbacks. Hide Caption 1 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Nyad faces the media in August 1978 before her first attempt to swim from Cuba to the United States. Hide Caption 2 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Nyad gets rescued from the water during her 1978 attempt. Hide Caption 3 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim –

Nyad holds a press conference in August 2011 in Havana, Cuba. Ocean swells, shoulder pain and asthma forced the swimmer to abandon her efforts at about the halfway point on this second attempt. Hide Caption 4 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Nyad jumps into the ocean at the Ernest Hemingway Nautical Club in Havana in September 2011. She was making her third attempt. Hide Caption 5 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Nyad prepares to leave Havana in August 2012 on her fourth try. Hide Caption 6 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Nyad waves before attempting the three-day, nonstop journey from Havana to Florida on Saturday, August 31. Hide Caption 7 of 8 Photos: Photos: Diana Nyad's long swim Diana Nyad's long swim – Nyad takes a drink after completing her 53-hour swim from Cuba to Key West, Florida, on Monday, September 2. Nyad is the first person to swim from Cuba to Florida without a shark cage. She completed the 110-mile swim on her fifth try. Hide Caption 8 of 8

At one point, she was vomiting because she had so much salt water in her system and was shivering. She sang lullabies to help her relax.

"It was really rough that first day, Saturday, after the start and I just said: 'Forget about the surface up. Get your hands in somehow, and with your left hand, say, push Cuba back, and push Florida towards you,'" Nyad said.

Through it all, she held her mantra close: "You don't like it. It's not doing well. Find a way."

'You are never too old'

Dozens of onlookers -- some in kayaks and boats, many others wading in the water or standing on shore -- gathered to cheer Nyad on as she finished the more than 100-mile swim.

She pumped her fist as she walked onto the beach toward an awaiting medic before being guided to an ambulance.

"I got three messages," an exhausted and happy Nyad told reporters. Her face was sunburned and swollen.

"One is we should never, ever give up. Two is you never are too old to chase your dreams. Three is it looks like a solitary sport, but it's a team," she said.

The swim was a long-awaited triumph for Nyad, who was making her fifth attempt since 1978 and her fourth since turning 60.

The first four tries were marked by gut-wrenching setbacks; if the rough, strength-sapping seas didn't force her to quit, an hours-long asthma attack or paralyzing and excruciating jellyfish stings did.

But for this swim, besides donning a suit meant to protect her against her jellyfish nemesis, she wore a special mask to prevent jellyfish stings to her tongue, a key factor in her failed attempt last year.

Nyad, who was 29 when she first tried the swim, said last week that she wanted to show that "you can dream at any age."

"This time, I am 64. So, the years of my life are shorter to the end," she said at a news conference in Havana on Friday. "So this time I am, all the way across ... going to think about all those life lessons that came up during the swim."

Fatigue almost seemed poised to derail her again early Monday.

About 7:30 a.m. ET, she was slurring her speech because of a swollen tongue and lips, her support team reported on its website.

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.

Divers swam 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.

'Tell me what your dreams are'

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 swam put 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 set out from Havana at 8:59 a.m. Saturday with a crew of 35, including divers to watch for sharks.

In her first attempt to cross the Straits of Florida in 1978, rough seas left her battered, delirious and less than halfway toward her goal.

She tried again twice in 2011, but her efforts ended after an 11-hour asthma attack and jellyfish stings.

Last year, she abandoned an attempt about halfway through after severe jellyfish stings and a lightning storm put her in danger.

Nyad was a swimming sensation before these attempts. In the 1970s, she won multiple swimming marathons and was one of the first women to swim around the island of Manhattan.

She was 8 years old when she first dreamed about swimming across the Straits of Florida. At the time, Nyad was in Cuba on a trip from her home in Florida in the 1950s, before Fidel Castro led a Communist takeover in Cuba and the country's relations with the United States soured.

The Los Angeles woman had said this was going to be her final attempt.

"I decided, this one no matter what happened, I don't want that experience again -- like right now, tonight -- talking to you about the journey is worth everything. It is. But I didn't want to be here packing up again," Nyad told CNN's Gupta.

She demurred when he described her as a hero but said she hopes she can serve as some sort of inspiration.

"I think that a lot of people in our country have gotten depressed, pinned in, pinned down with living lives they don't want," Nyad said.

She continued: "I do write all the time about -- you tell me what your dreams are. What are you chasing? It's not impossible. Name it."