Bora-Hansgrohe’s three-time world champion picked up the 12th Tour de France stage win of his career with a trademark flexing of muscles at the conclusion of the undulating 175.5km stage through Alsace in easternmost France.
European champion Trentin opened up the sprint after being launched by his Mitchelton-Scott teammate Daryl Impey, but Sagan surged through on the other side of the road to win by a bike length.
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Van Aert’s second place earned the Jumbo-Visma rider six bonus seconds and slashed his deficit to 14 seconds on yellow jersey Julian Alaphilippe of Deceuninck-QuickStep. The Frenchman sneaked into the top 10 but didn’t have the sprinting legs to push Sagan for the win.
Italy’s Sonny Colbrelli (Bahrain Merida) and Belgium’s Greg Van Avermaet (CCC Team) completed the top five while Australia’s Michael Matthews stuttered to seventh despite some hefty work by his Sunweb team in the closing kilometres.
Strong tempo setting by Sagan’s Bora team split the peloton on the penultimate climb of the day, ensuring that Stage 4 winner Elia Viviani and all the pure sprinters were taken out of contention.
Portuguese veteran Rui Costa, the 2013 world champion, put in a brave solo dig inside the final 10km but the UAE Team Emirates rider was reeled in with 2km remaining.
Sagan looked to be positioned well back in the pack but his experience shone through, the 29-year-old powering through when it mattered to take his first win of the race and move 47 points clear at the top of the green jersey standings.
There were no changes in any of the other classifications with Van Aert retaining the white jersey as best young rider and Belgium’s Tim Wellens (Lotto Soudal) extending his lead in the polka dot jersey standings after starring in the day’s break.

Full highlights of a Sagan masterclass in Stage 5

Stage 5: Saint-Die-des-Vosges to Colmas - how it happened

The consistently undulating stage through the forests of the Vosges and the manicured vineyards of Alsace featured four categorised climbs and numerous leg-sapping hills.
A fierce battle ensued for the opening 30km with Lotto Soudal pair Thomas De Gendt and Wellens taking it in turns to force moves.
Stage 5: live comments and analysis
Eventually Wellens was the instigator of a move that stuck, the Belgian in polka dots joined by Germany’s Mads Würtz Schmidt (Katusha-Alpecin), Australia’s Simon Clarke (EF Education First) and Latvia’s Toms Skujins (Trek-Segafredo).
The quartet never built up an advantage of much more than two minutes, largely thanks to the patrolling pace-setting of Sagan’s Bora-Hansgrohe team on the front of the peloton.
Wellens picked up maximum points on the first two climbs, the Cat.3 Cote de Grendelbruch and the Cat.2 Cote du Haut-Koenigsbourg, to consolidate his lead in the KOM competition.
In between those climbs, the intermediate sprint was won by Australian veteran Clarke before Italy’s Elia Viviani pipped Sagan when the pack darted through, reducing the Slovakian’s virtual lead in the green jersey competition by a single digit. Not that this would matter come Colmar.

Elia Viviani wins the peloton sprint

The race exploded into action on the Cat.2 Cote de Trois-Epis with 40km remaining when the peloton split in two and the break broke apart.
After Würtz Schmidt was the first escapee to feel the heat, Skujins rode clear of Wellens and Clarke - the Latvian national champion cresting the summit with a small gap over the Belgian in pursuit.
Behind, Bora’s hefty pacing paid dividends when the likes of Viviani and fellow pure sprinters Caleb Ewan, Alexander Kristoff and Dylan Groenewegen all distanced on the climb - further improving the chances of Sagan for the stage win.
By the time the riders hit the final climb, all the escapees bar Skujins had been swallowed up by the peloton. The Latvian was taken shortly after with 22km remaining - not before the likes of Simon Yates, Ilnur Zakarin and Edvald Boasson Hagen had all been spat out the back.
Sunweb took up the pacing for their man Matthews, while Team Ineos came to the front to keep their GC riders Geraint Thomas and Egan Bernal out of trouble.
After a remarkable fight back on the descent, Boasson Hagen returned to the peloton just as Portuguese veteran Rui Costa (UAE Team Emirates) darted clear with 7km remaining.
Costa built up a lead of 12 seconds but was soon shaking his head as the peloton rampaged past with 2km remaining.
Sunweb and Bahrain Merida flocked to the front for Matthews and Colbrelli before Daryl Impey, the South African champion, put in a solid shift to launch Trentin to the line.
Trentin went shoulder to shoulder with Belgian Jasper Stuyven (Trek-Segafredo) but Sagan showed his class with a powerful surge to win at a relative canter. His belated first win of the race came after three finishes in the top five. For all his efforts, Norway's Boasson Hagen finished eleventh.

Passionate Sagan explains how he secured his impressive stage win

"You just have to be patient and the victory will come,” Sagan said. “I have to say thanks to all my teammates, they did a very great job. Finally a Tour de France victory came for us, it's very nice. We controlled the race all day, on the flat part until the finish.
"I did my best and it came. If I don't win, then everybody will ask me what is missing. You can see, nothing is missing. It's just everybody needs good luck and a good day for a win."

Stage 6: Mulhouse to La Planche des Belles Filles
Seven categorised climbs and the race’s first summit finish await the riders in the toughest stage of the Tour so far - a 160.5km ride from Mulhouse to La Planche des Belles Filles in the Vosges Mountains.
Alaphilippe holds a 14-second lead over Van Aert going into this first showdown between the race favourites - but realistically, neither rider can expect to be in their respective yellow and white jerseys by the end of play.
With Jumbo-Visma duo Steven Kruijswijk and George Bennett lurking at 25 seconds, and Team Ineos riders Bernal and Thomas at 40 seconds and 45 seconds respectively, Stage 6 should coax the favourites into showing their hands on a finish that comes on a steep dirt track one kilometre beyond the usual summit finish.
Elsewhere, Wellens will face a battle to keep hold of the polka dot jersey on a day that has 44 KOM points up for grabs. The Belgian currently leads with 17pts against Skujins’s 9pts.
In short: on Thursday, the battle really begins.
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