Two protesters were killed in demonstrations in Cairo, two in Buheira and one in Alexandria, officials said.
Egyptian authorities tightened security in Cairo and other cities in anticipation of further protests. Police sealed off several main squares in Cairo, including Tahrir which was the centre of the 2011 uprising, and beefed up security at vital state installations.
In another incident, a homemade bomb went off in Alf Maskan district in Cairo injuring two policemen.
The anniversary this year is the first under the rule of Abdel Fattah el-Sisi as President.
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Islamists had called their supporters for protests all over the country to revive "the revolution".
The same day also marks the Police Day.
However, the country has cancelled the celebrations of the Police day as it is in a seven-day mourning for the death of Saudi King Abdullah, who passed away on Friday.
Meanwhile, two militants were killed while they were trying to plant a bomb on el-Anani Bridge in Behaira governorate, officials said.