Censor.NET reports citing AFP.
The five countries ran unopposed for the non-permanent seats after regional groups put them forward as their choice, but the contenders still had to garner two-thirds of votes cast.
Applause and cheers broke out in the assembly hall after first results showed Senegal had won the largest share, picking up 187 votes followed by Uruguay which garnered 185.
Egypt won 179 votes and Ukraine 177 in the 193-nation assembly.
The newly-elected members will begin their two-year stint on January 1, replacing Chad, Chile, Jordan, Lithuania and Nigeria.
They will join the other five non-permanent council members: Angola, Malaysia, New Zealand, Spain and Venezuela.
The election to the Security Council came as UN diplomacy has been overshadowed by tensions with Russia and bloodshed in the Middle East.