Three car bombs exploded near offices of the labour, interior and finance ministries and a suicide attacker in a car struck a police patrol in Dora, in southern Baghdad.
The first explosion in the centre of Baghdad was heard at 10.25am local time, another came within seconds and a third blast occurred a minute later.
An interior ministry official said 12 of those killed by the suicide attacker in Dora were students at a nearby technical college. The other three fatalities were policemen.
The fifth car bomb targeted a courthouse in Mansur, western Baghdad.
Violence across Iraq dropped dramatically last month, with the fewest deaths in attacks recorded since the US-led invasion in 2003.
Official figures showed a total of 122 people were killed in November.
However, the Baghdad government and the US military have warned of a rise in attacks in the run up to the election, which will take place on 6 March.
