He lost two hours waiting for assistance before continuing but, with co-driver Daniel Elena in pain from the jolt in the dunes, had to accept defeat.
"The sand was extremely loose. We got stuck once and managed to get going again," Loeb told the Dakar.com website before retiring.
"We got to a crest where another car was stuck. We were following Nasser (al-Attiyah) and saw him go over, so we did the same, but I hadn't realised there was a hole behind the crest. And, bam, we went right into the hole.
"Right now I'm trying to see how my co-driver's doing: we're driving really slowly and, as soon as I go over 30 kph he screams inside the car," added the Frenchman.
Peterhansel, Loeb's team mate who had been nearly seven minutes clear on Tuesday and is heading for a record 14th Dakar win, took the stage to extend his lead over Spaniard Carlos Sainz to 31 minutes and 16 seconds.
Sainz, also in a Peugeot and a double world rally champion, got bogged down in the dunes early on and was 18 minutes behind Peterhansel at the finish.
Dutch driver Bernhard Ten Brinke was third in a Toyota, but more than an hour and a quarter off the pace, with Qatari Nasser al-Attiyah fourth.
In the bikes category, Yamaha's French rider Adrien van Beveren stayed on top in a stage won by Honda's Spaniard Joan Barreda. Argentina's Kevin Benevides was in second place, a minute behind the leader.
Thursday's sixth stage, with a 313km timed special section, runs from the city of Arequipa and up to the shores of Lake Titicaca before ending in La Paz.
(Reporting by Alan Baldwin in London, editing by Ed Osmond)
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