The 13-12 loss Sunday means the Dodgers will have to win the next two at home if they hope to regain the title they last held in 1988.
The game was a nailbiting, back-and-forth hitting contest, with multiple lead changes that kept fans breathless and glued to the action through extra innings. It stretched out more than five hours into the early morning in Houston.
It also set or tied several records. In only five games, this World Series has now broken a record for most home runs - 22 - combined by both teams in a series, with the previous record at 21 set over seven games when the Angels beat San Francisco in 2002.
Starting pitcher Clayton Kershaw said Los Angeles can bounce back in the next game.
"It's not a matter of character or effort," Kershaw said following the loss. "This clubhouse has shown time and time again they can overcome adversity."
Dodgers fans were disappointed with the loss but looking forward to the World Series returning Tuesday to Dodger Stadium.
"It was a hard-fought game," said Dodger fan Fidel Romero, who watched the game at a viewing party near downtown Los Angeles. "It just kept going up and down. We kept scoring, taking the lead. They kept coming back. But it is the World Series. It's not easy.
Added another diehard fan: "We're not out of it. I believe in my guys."
The Dodgers twice took big leads only to have the Astros catch up and then overtake them in the seventh. LA caught back up again in the top of the ninth, evening the score at 12-12 off an RBI by Chris Taylor.
The game went into the 10th inning tied at 12-12. With star reliever Kenley Jansen pitching, Alex Bregman hit an RBI single for the 13-12 win.
As it ended, the raucous Houston crowd began chanting "Beat LA, beat LA."
The five homers by Houston at Minute Maid Park in Game 5 also matched the most hit by a team in a World Series game. The Dodgers had two.
It was also the highest-scoring game of the 2017 postseason.
The 25 combined runs was also the second-highest combined team scoring total in a World Series game, with the current record standing at 29, set in 1993 when Toronto beat Philadelphia 15-14.
To start the matchup, Los Angeles jumped out to an early 3-0 lead in the first inning with hits by Logan Forsythe and Chris Taylor, plus two walks and a throwing error by Astro first baseman Yuli Gurriel.
Forsythe lined a slider into left field as two runs scored. The ball bounced off the heel of Marwin Gonzalez's glove, allowing Justin Turner to come home without a play.
They took a 4-0 lead into the fourth inning, but couldn't hold on to it.
An RBI double by Carlos Correa and three-run homer by Yuli Gurriel tied it at 4-4.
For the Dodgers and their fans, that Gurriel home run particularly stung.
The Astros first baseman also hit a home run in Game 3, but became a controversial figure when he made a racist gesture mocking the Asian heritage of Dodgers pitcher Yu Darvish.
Gurriel was suspended for five games next season, but not for the World Series itself, as some Dodgers fans had wanted to see.
The World Series returns to Dodger Stadium for Game 6 on Tuesday and if necessary Game 7 on Wednesday.
Justin Verlander is expected to pitch for Houston, with Rich Hill on the mound for Los Angeles.
Former President George W. Bush threw out the ceremonial first pitch before Game 5 with father and former President George H.W. Bush on the field cheering him on.
The younger Bush was a former controlling owner of the Texas Rangers, but donned an Astros jacket and received a round of applause when he stepped on the mound.
The elder Bush, who is 93 and in a wheelchair, was handed a ball when he came onto the field. The one-time Yale first baseman held it with a perfect grip as the crowd cheered.
The Associated Press contributed to this report.