(Adds death toll rising to 26 from 22 after fifth bombing)
BAGHDAD, July 19 (Reuters) - Five car bombs killed 26 people in mostly Shi'ite Muslim neighbourhoods in Baghdad on Saturday, police and medics said.
The first explosion, a suicide car bombing, killed seven people at a police checkpoint in the Abu Dsheer district in the south of the capital, the sources said.
Four other car bombs killed a total of 19 people: one in the Bayaa district in southwestern Baghdad, one in the western district of Jihad and two in northern Baghdad's Kadhimiya, which boasts a major Shi'ite shrine.
The army and allied Shi'ite militia are trying to push back Sunni insurgents who swept through northern Iraq last month to within 70 km (45 miles) of Baghdad.
Militants fought off an army offensive to retake the northern city of Tikrit on Tuesday. The army was forced to pull back south of the city on the banks of the Tigris.
The fighting has exacerbated a political crisis in Baghdad, where Shi'ite caretaker Prime Minister Nuri al-Maliki is trying to form a government in the face of opposition from Sunnis, Kurds and some Shi'ites, three months after Iraq held a parliamentary election.
Iraq's Shi'ite clergy as well as Western powers have pressed politicians to overcome their deadlock and agree a new unity government to help tackle the insurgency and prevent Iraq from splitting down ethnic and sectarian lines. (Reporting by Raheem Salman; Editing by Louise Ireland)