Kristoff started his sprint from the very front of the bunch after his Katusha team had set a vast pace in the lead-out, but was forced to make his move a little early as the last domestique peeled off some way from the finish line.
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Sagan rode in the Norwegian’s slipstream and attempted to overtake him in the last 50 metres or so, but Kristoff, despite already having expended some effort, was able to hold him off.
Niki Terpstra (Etixx-Quick Step) held onto the overall lead, though he suffered a scare with 6km to go when Katusha used the strong winds to force a split in the peloton.
Kristoff and three of his domestiques, along with six other riders, managed to open a gap ahead of the peloton, and looked initially as though they would put time into the others – however, most of the favourites managed to haul themselves back into the lead group with 2km to go.
The wind played a large part in proceedings all day long. There was action right from the start as the peloton split into groups, with second-placed overall Maciej Bodnar (Tinkoff-Saxo) caught out. A long chase ensued, but Bodnar’s group managed to make contact again with the lead group with 90km to go.
Following the catch the pace in the peloton slowed, allowing a group of five – Ben Hermans (BMC), Marco Haller (Katusha), Jelle Wallays (Topsport Vlaanderen-Baloise), Dmitriy Gruzdev (Asanat) and Mathew Hayman (Orica-GreenEdge) – to break clear. They did manage to build up a lead big enough for Hayman to be virtual leader for a little while, but were caught with plenty of time to spare.
Terpstra now has just one more day to hold off the challenges of Bodnar (still six seconds behind), a rampaging Kristoff (now third overall) and Sky’s Ian Stannard (12 seconds behind) to seal the overall win.
Britain’s Luke Rowe (Sky) lost his lead in the best young rider’s classification as Sagan moves up to sixth overall.
It was bad news for Lars Boom (Astana): the Dutchman was disqualified from the race for drafting behind a team car.
Tour of Qatar 2015, stage five: Al Zubarah Fort to Madinat Al Shamal, 153km
1. Alexander Kristoff (Nor) Katusha in 3-03-01
2. Peter Sagan (Svk) Tinkoff-Saxo
3. Nikias Arndt (Ger) Giant-Alpecin
4. Tom Boonen (Bel) Etixx-QuickStep
5. Adam Blythe (GBr) Orica-GreenEdge
6. Heinrich Haussler (Aus) IAM Cycling
7. Jose Joaquin Rojas (Spa) Movistar
8. Arnaud Demare (Fra) FDJ
9. Greg Van Avermaet (Bel) BMC Racing
10. Nacer Bouhanni (Fra) Cofidis all same time
17. Ian Stannard (GBr) Sky at same time
22. Luke Rowe (GBr) Sky at same time
Overall classification after stage five
1. Niki Terpstra (Ned) Etixx-QuickStep
2. Maciej Bodnar (Pol) Tinkoff-Saxo at 6 secs
3. Alexander Kristoff (Nor) Katusha at 11 secs
4. Ian Stannard (GBr) Sky at 12 secs
5. Greg Van Avermaet (Bel) BMC Racing at 19 secs
6. Peter Sagan (Svk) Tinkoff-Saxo at 31 secs
7. Luke Rowe (GBr) Sky at 33 secs
8. Heinrich Haussler (Aus) IAM Cycling at 39 secs
9. Andriy Grivko (Ukr) Astana at 41 secs
10. Tom Boonen (Bel) Etixx-QuickStep at 42 secs