Adam Taylor/ABC

The remaining five celebrities on ABC’s “Dancing With the Stars” had their toughest challenge yet tonight, when they had to perform one routine plus a second, “instant” jive to music that they hadn’t heard before.

And the stars came out in full force tonight, carrying their “A” games and earning high scores, including the first double perfect scores of the show’s season 13.

Rob Kardashian earned kudos for his snappy quickstep. Judge Carrie Ann Inaba told him he was the ideal contestant on the show because even though he started off poorly, he’s had continuous improvement.

“Tonight, you’re polished, you’re elegant, you’re smooth and you were light on your feet,” she said.

Inaba, Bruno Tonioli and head judge Len Goodman each gave Kardashian nine points, leaving him with a total 27 out of 30 —  his highest score of the entire competition.

Immediately after his routine, he drew his instant dance song — Hall and Oates’ “Maneater.”

After their initial performances, contestants would each draw a song at random, learn the routine in 20 minutes and then perform it.

Kardashian’s second dance also earned him positive reviews. Goodman told him the jive needed sharper kicks, but overall commended the routine. He earned 24 points, for a grand total of 51.

Hope Solo and Maksim Chmerkovskiy’s first dance, also a quickstep, won them 27 points. It was their highest score of the competition.

In the short video piece before their dance, Chmerkovskiy – who has caught flak for being too outspoken to Goodman and too rough with Solo — said he wanted to take a “gentler” approach to tutoring his partner. The approach seems to have worked.

“It was a blend of speed and control,” Goodman said of the performance, telling the World Cup soccer player that she’d “fulfilled her potential.”

Solo’s instant jive — to “The Best Damn Thing” by Avril Lavigne — earned a surprisingly enthusiastic review from Goodman, who said her energetic performance was “everything a jive should be.”

While the other judges gave her an eight, Goodman awarded her a nine, for a total of 25 and a grand of 52 points.

Former talk show host Ricki Lake earned 28 points for her first dance, an airy waltz.

Goodman praised Lake’s lines and interpretation but faulted her for imprecise footwork, saying that his heart wanted to give her a perfect score – 10 – but that she’d never earn it unless her footwork improved.

But Tonioli gave Lake’s waltz full marks, calling her performance “deliciously dreamy.”

For her instant dance, she drew “Land of 1,000 Dances” by Wilson Pickett, and judges felt it lacked her usual seamless fluidity. Inaba told Lake that at times it appeared that she stopped dancing while her partner kept on going, but Goodman told her that she “coped very well” with a difficult dance.

She earned 24 points for the jive, tying with Solo for a grand total of 52 points and second place.

Nancy Grace earned positive feedback – and 24 points — for her saucy first-round tango. For her instant jive, the TV host drew “Upside Down” by Paloma Faith – finishing up with a cartwheel.

Despite that final flourish, her second routine seemed to fall flat, earning her 20 points and a grand total of 44 for the night. Goodman told her that hers was a Cinderella story.

“You’ve come to the ball, and you’ve lasted eight weeks, however, for me, it’s midnight and it’s time to go home,” he said.

Fan favorite J.R. Martinez and partner Karina Smirnoff delivered an ethereal waltz that brought the ballroom audience to its feet in rousing applause. Inaba called the performance “magic.”

Martinez and Lake have both been battling for the top spot on the leaderboard, but last week he slipped several notches to land in the middle of the pack. Tonight he achieved his ultimate goal, earning the season’s first 30 points for his waltz.

Martinez, an actor and Iraq war veteran, ecstatically – and jokingly — thanked his mother and Justin Bieber, and then drew the song “Tutti Frutti” by Little Richard for high-energy instant jive that earned him his second 30 points and second standing ovation of the night.

“Your side kicks were sensational. Your timing was impeccable. You’ve got it man! You’ve got it!” Tonioli raved.

Tomorrow one star will be voted off the show.

Elimination in the competition results from a combination of judges’ scores and audience votes. The celebrity with the lowest combined scores is sent home, until three stars remain. They and their partners compete for the championship.

Actor David Arquette – a crowd favorite – was eliminated from the show last week. The other celebrities who were voted off before him were activist Chaz Bono, fashion guru Carson Kressley, singer Chynna Phillips, reality TV star Kristin Cavallari, Italian model Elisabetta Canalis and NBA star Metta World Peace (formerly Ron Artest).

Tonight’s Scores

Ricki Lake and Derek Hough: 28; 24. Total: 52/60

J.R. Martinez and Karina Smirnoff:  30; 30. 60/60

Rob Kardashian and Cheryl Burke: 27; 24. Total: 51/60

Hope Solo and Maksim Chmerkovskiy: 27; 25. Total: 52/60

Nancy Grace and Tristan MacManus: 24; 20. Total: 44/60