Dumoulin beat out fellow Frenchmen Bryan Cocquard (Europcar) and Mathieu Drujon (BigMat-Auber 93) to win the 69km journey to Ales Ales.
Jerome Cousin, winner of two stages for Europcar, remains ahead in the general classification ahead of the sixth and final stage later on Sunday.
“Obviously, I’m happy with this victory," Dumoulin said.
"This morning, our strategy was to be offensive to prevent being trapped in a split caused by the wind. I hadn't good sensations at the start and I have been caught in the rear of the split. I was not in an ideal physical condition.
"Fortunately, Maxime, Romain and Axel were in the first group. Behind this group, several teams have piled on the pressure to get back on to the front of the race. There was a lot of wind today and small roads.
"My team-mates gave me a hand up taking a pull at the front but I was not serene close to the finish line. Romain and Maxime helped me in last kilometers whereas Europcar’s riders were leading the pack to prepare the sprint for Bryan Coquard.
This morning at the briefing, we watched and studied the final part of the race, in particular the last roundabout. This is there, at 500 meters from the finish, that I anticipated and so, I was able to make a difference and to go to win.”
Stage five results:
1 DUMOULIN Samuel AG2R La Mondiale 16 20
2 COQUARD Bryan Europcar 11 12
3 DRUJON Mathieu Auber 93 6 7
4 PATOUX Cyrille Roubaix - Lille Métropole 5 5
5 KOCJAN Jure Euskaltel - Euskadi 4 4
6 BOUET Maxime AG2R La Mondiale 2 3
7 ROUX Anthony Equipe Cycliste FDJ 2
8 VAN HOECKE Gijs Topsport Vlaanderen – Baloise 1
9 WESTRA Lieuwe Vacansoleil - DCM
10 DECLERCQ Tim Topsport Vlaanderen – Baloise