There was no immediate claim of responsibility. In the past, such attacks in the Eastleigh area of Nairobi have been blamed on Somalia's al Shabaab Islamist group, which attacked a Nairobi shopping mall in September and killed at least 67 people.
"Police are securing the area for emergency response services," the disaster organisation said on its official Twitter site.
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Nine people were critically injured, it added.
Nairobi's police commander Benson Kibui told Reuters the incident might have involved twin blasts. He confirmed the five dead and said he was seeking confirmation of a sixth killed.
Ambulances and private cars ferried injured to hospital, a witness said.
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On Sunday, a man suspected of assembling a bomb was killed when it went off where he lived near Eastleigh, Kenyan newspapers reported.
The Standard daily, which cited police and witnesses, had said three men who lived with the victim fled in a car shortly after Sunday's blast.