Kirsipuu, a member of the AG2R Prevoyance team, finished the 123.03-mile leg from Soissons to Rouen in 4:13:33, edging Michael Sandstod of Denmark and Ludo Dierckxens of Belgium in a sprint to the finish line.
"It was a very difficult sprint because everyone attacked in the last kilometers," said Kirsipuu, who has nearly 100 professional victories.
The peleton finished 33 seconds off the pace.
Among those in the group were Galdeano and three-time defending champion Lance Armstrong. Galdeano, who grabbed the overall lead in Wednesday's team time trial, retained his four-second advantage over countryman Joseba Beloki. Armstrong remained third, 17 seconds behind, after one of the flattest stages of the 20-stage event. Friday's sixth stage is more than 123 miles from Forges-les-Eaux to Alencon.
Kirsipuu duplicated his effort of a year ago, when he followed a disappointing team time trial by winning a stage. The Estonian champion was the slowest rider in Wednesday's test after being dropped midway through the leg.
As expected, Thursday's stage began with an early break, led by Russian Vjatceslav Ekimov of Armstrong's U.S. Postal Service team. But the peleton caught the escapees shortly thereafter. Surprisingly, another group of riders broke free from the pack midway through the race, with five building a lead of nearly five minutes with a quarter of the race to go.
The peleton halved the lead before a huge crash took out some 20 riders. Despite a series of attacks from the pursuers, the race ended in a group sprint, with Kirsipuu beating Sandstod and Dierckxens to the finish line.
"My legs almost let me down," Kirsipuu said. "At the end, I wasn't a real sprinter anymore. I hadn't any stage victory expectations. It's a great relief for me and for the team, who can now concentrate on the mountains."
Kirsipuu, who turns 33 next week, is fully recovered from a serious knee injury suffered in March, capturing his third career Tour de France stage victory. Galdeano's ONCE team and Armstrong's U.S. Postal Service squad perfectly controlled the race, knowing the breakaway riders could not affect the overall standings.