If it takes 27.3 days for the moon to

make 1 revolution around the Earth,

why does it take a total of 29.5 days

to complete 1 set of phases?

It takes 27.3 days for moon to make one revolution this is called sidereal month and it takes 29.5 days to complete a cycle of phase this is called synodic month. The synodic month is difference is because as the moon moves around earth, the earth is also moving round the sun. Hence, the moons needs to move farther away to make up the distance that was added as the earth also revolves in other to complete the cycle.