The man, identified as 27-year-old Mohammed Yasser Yaqub, was killed in a car near junction 24 of the M62 in Huddersfield at around 6 PM yesterday, The Telegraph reported.
The incident is not terrorism related, the police said.
Images from the scene showed a silver Audi with bullet holes in its windscreen and bonnet.
West Yorkshire Police confirmed there were five arrests during the operation - three at the scene and another two from a related stop of another vehicle in the Chain Bar area of Bradford at around the same time.
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The case is being referred to theIndependent Police Complaints Commission (IPCC), which said its investigators were at the scene.
On its Twitter account, the IPCC said: "The man's family has been informed. This is the early stage of the investigation and we will provide further updates when we have them."
Gemma Wilson, Lindley Councillor, told Sky News: "I assumed at first it was a crash but realised if it was, it was a major one due to the volume of police in the area and the wide area that was cordoned off.
A West Yorkshire Police spokesman said: "Around 6 PM last eveningduring a pre-planned policing operation near to the M62 in Huddersfield a police firearm was discharged and a man has died."
West Yorkshire Police are "fully co-operating" with the IPCCinvestigation, he added.
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