GUWAHATI, India, Nov 5 (Reuters) - Five people were killed and a dozen wounded when two powerful bombs exploded in troubled northeast India's biggest city Guwahati on Sunday, police said. The first bomb exploded in a crowded market in the heart of the city, killing three people and wounding 10, three of whom were said to be in a critical condition. Police said the bomb exploded in front of a sweet shop in the busy Fancy Bazar area of Guwahati, the main city of Assam state. A second bomb went off outside an oil installation on the outskirts of the city killing two people. Three others were injured in the explosion. "Both the bombs were powerful and we are yet to identify who is behind this incident," senior police officer Nitul Gogoi said. Assam has been home to a nearly 30-year-old insurgency led by the United Liberation Front of Asom (ULFA) which is fighting for an independent homeland. Tens of thousands of people have died in the revolt. The ULFA and the Indian government called off their peace talks in September after New Delhi ended a truce with rebels. Violence has since increased in the oil- and timber-rich region.