Four of the soldiers died at the scene and the fifth died later from wounds, the military said in a statement. The blast also wounded three U.S. soldiers and an Iraqi interpreter.
Iraqi police said the soldiers had been walking in the Mansour district when a suicide bomber wearing an explosives vest walked up to them and blew himself up.
"He came and stood beside them and started talking to them and then detonated himself," an Iraqi Army officer at the scene told the New York Times.
An Iraqi police officer at the scene, also speaking on condition of anonymity because he was not authorized to speak to the media, told news agencies two civilians were also killed and another eight wounded in the attack.
Col. Allen Batschelet, chief of staff for U.S. forces in Baghdad, said in the statement that the attack would not deter the military from working jointly with Iraqi forces "to protect the Iraqi people against terrorists, extremists and criminals."
"Five soldiers paid the ultimate sacrifice on behalf of the Iraqi and American people. We are firm in our resolve to protect the people of Iraq and kill or capture those who would bring them harm."
In another attack Monday, a suicide bomber killed a prominent Sunni Arab tribal chief who headed a neighborhood security unit and three others in the volatile Iraqi province of Diyala.
Police said the bomber, a woman, went to the home of Thaer Saggban al-Karkhi in Kanaan, knocked on the door and told guards she needed to speak to him.
When Karkhi came to the door she detonated a vest packed with explosives hidden underneath her robes, police said. Karkhi's 5-year-old niece, a cousin and a security guard also were killed.
There was no immediate claim of responsibility, but al-Qaida in Iraq has been targeting fellow Sunni Arabs who have taken up arms against the militants and joined the so-called "awakening councils" -- like the one al-Karkhi led, according to the Associated Press.
Also Monday, a suicide car bomber blew himself up in front of a large hotel in the Iraqi province of Sulaimaniya, wounding 13 people, provincial governor Dana Ahmed said.
Dana Ahmed said the explosion damaged the front of the Sulaimaniya Palace Hotel, the biggest hotel in the province and a frequent meeting place for officials.
U.S. military spokesman Rear Adm. Greg Smith said on Sunday that a recent increase in bombings in Iraq was not the start of a wider trend and that violence was down overall, according to Reuters.