Dutchman Tom Dumoulin retained the overall leader's Maglia Rosa (pink jersey) after finishing safely in the pack, although Luxembourg's Bob Jungels took four seconds off his lead which now stands at 16.
Tuesday's winner Diego Ulissi is a further four seconds adrift in third place on general classification.
FDJ's Frenchman Arnaud Demare won the battle for second place in the stage ahead of Italy's Sonny Colbrelli who is riding for Bardiani Valvole.
The second longest stage in this year's race proved relatively straightforward and incident-free although a 6.5km circuit of Benevento at the end proved chaotic, with Griepel's fellow German Marcel Kittel unable to mount a challenge.
Earlier a breakaway group had grabbed a seven-minute lead on the peloton but were reeled in with 20km to go.
Kittel won two stages early in the race, which this year started in the Netherlands.
Thursday's sixth stage features two summit finishes and will offer the first chance for GC favourites such as Astana's Vincenzo Nibali to flex their muscles.
(Reporting by Martyn Herman; Editing by Catherine Evans)
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