Bogita Ongeri said authorities recovered 100kg (220 pounds) of TNT from the vehicle which was intercepted at Dolo, along Kenya's border with Ethiopia on Saturday.
Ongeri said security forces had been tracking the car which has Kenyan registration and were aware that the suspected terrorists had unsuccessfully attempted to gain entry into Kenya at another border point. He said the five killed are suspected members of the Somali militant group al-Shabab, which is allied to al-Qaida. Al-Shabab has vowed to carry violent terrorism in Kenya because Kenyan troops are in Somalia fighting the militants. Kenya sent its troops into Somalia in Oct 2011 to fight al-Shabab after the Kenyan government blamed the extremist rebels for a series of cross-border attacks including the kidnapping of four western nationals.
Al-Shabab are waging an insurgency against Somalia's weak U.N.-backed government which is bolstered by African Union troops.
The militants claimed responsibility for the attack on Nairobi's Westgate Mall a year ago in which more than 67 people were killed by four Somali gunmen.
In March, Kenyan authorities with the help of the FBI, intercepted an SUV at the Kenyan coast with 173 kilograms (381 pounds) of explosives. Kenya police said two men, arrested March 11 in the car spoke on the phone with militants in Somalia connected to the Westgate Mall attack.
Police believe the SUV was to be used as part of a three-pronged coordinated attack on the Mombasa International Airport at the coast, the ferry crossing and a shopping mall.