The first attack took place in Baghdad's Uveyric neighborhood where an explosion killed two people and wounded seven others.
The second explosion in El-Husseini neighborhood left three people dead and four others wounded.
No group has claimed responsibility for either attack so far, but Iraqi officials blame ISIL.
Iraq has been gripped by a security vacuum since June 2014 when ISIL militants stormed the northern province of Mosul and declared a self-styled caliphate in parts of Iraq and Syria.
Prime Minister Haidar al-Abadi had lifted Baghdad’s eight-year curfew on Feb. 7./