Spectators surrounded Diana Nyad as she reached the shore of Key West, Fla. on Monday after her 110 mile swim from Cuba.

MIAMI — Her speech slurred and her face red and swollen, Diana Nyad conquered the treacherous Florida Straits on Monday and completed a 53-hour, 110-mile swim from Cuba to Key West.

Ms. Nyad, a 64-year-old endurance swimmer, now becomes the only person to have succeeded in swimming from Cuba to Key West without a shark cage. With her final stroke into Smathers Beach in Key West, Ms. Nyad proved that perseverance and big dreams can transcend age and injury.

This was Ms. Nyad’s fifth attempt in 35 years to swim without fins or a wet suit from Cuba to Key West, a daunting journey laden with so many encumbrances, including swarms of jellyfish, that until Monday it seemed impossible to overcome.

Her official time was 52 hours 54 minutes 18.6 seconds, according to her Web site.

“I have three messages,” Ms. Nyad, her face scorched and puffy from so many hours in the saltwater, said as she leaned on her best friend. “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 takes a team.”

After two nights and two days of being buffeted by ocean waves, she walked on to Smathers Beach on Monday at 1:20 p.m. to the cheers of onlookers and her 35-member support team. Her team had kept a close watch on Ms. Nyad from five boats that trailed her during the swim.

Millions more exhilarated in her age-defying feat from afar, on Twitter and Facebook, viewing it with inspiration and pride.

One of the first to send a message on Twitter was President Obama: “Congratulations to Diana Nyad. Never give up on your dreams.”

The ocean between Florida and Cuba is a notoriously fierce opponent, brimming with sharks, jellyfish, squalls and an uncompromising Gulf Stream current.

Last year, Ms. Nyad was defeated by all three. She was forced back on to the boat after storms knocked her off track, sharks menaced her and she was badly stung by box jellyfish. In 2011, her shoulder injured, she suffered her first asthma attack in the water and began to vomit, a turn of events that forced her to stop.

Each time Ms. Nyad vowed it would be her last. But she could not help herself. The swim across the Straits was her personal quest, one that until Monday seemed Quixotic, at best, and fatuous, at worst.

But this year nature tipped its hat.

Sharks steered clear, the swift current carried her along and storms took the Labor Day weekend off. Even the box jellyfish cooperated, although she was well prepared for their challenge. She wore a jelly protection suit and a mask to protect her face from their poison. Her body was coated with “sting stopper” gel to serve as a barrier from the venom. When she encountered box jellyfish near Key West, Ms. Nyad’s divers swam ahead of her this year to disperse them.

“I think that Mother Nature said: ‘You know what? Let her go,’ ” said Bonnie Stoll, one of her closest friends. “Diana also did her homework.”

To stay focused, Ms. Nyad did what she always does: she hummed her favorite songs in her head. Her strokes were calibrated to the cadence of the Beatles’ “Ticket to Ride” and “Paperback Writer” to name two.