The U.S. State Department condemned the attacks in a statement Friday and urged "all Egyptians to exercise calm and restraint ahead of the third anniversary of Egypt's revolution" and offered support of "their political transition."
The latest explosion, at the Radobis Cinema Theater in the Haram district of Giza, killed at least one person, Ahram Online reported.
Earlier, four people were killed and 76 injured at the Cairo Security Directorate building near the center of Cairo about 6:30 a.m., local time, the Health Ministry said.
A vehicle loaded with explosives stopped suddenly in front of the building before exploding, Ahram Online reported.
The blast blew out windows and damaged a portion of the building's facade, state television said.
The nearby Museum of Islamic Art building also was damaged, as well as some of the artifacts inside, the minister of state for antiquities said.
A bomb, thrown at a police vehicle near a metro station in Giza, killed one person, deputy Giza security chief Mahmoud Farouk said. Eleven people were injured in the attack.
A bomb that exploded at a police station in Giza caused no casualties, the Wall Street Journal reported.
"It's a vile, desperate attempt by evil terrorist forces to disrupt the success Egypt and its people have achieved in the [transitional] road map and the passing of the new constitution," Prime Minister Hazem el-Beblawi said in response to the Cairo bomb.
No group had claimed responsibility for the attacks.