Is it common to see 5 shooting stars in less than half an hour and in the same area of sky?

Answer 1

That's not uncommon at all. In a "meteor shower" you might see five in a MINUTE and it not be unusual.

Meteor showers are the remnants of old dead comets. As the comet comes past the sun in its orbit, it sheds dust and pebbles nearby, and some of these are a little slower and some a little faster, but still pretty close to the same orbit. Some of these orbital paths happen to intersect Earth's orbit and when Earth comes through the path, we have a meteor shower.

Because Earth's orbit is remarkably stable and regular, Earth passes repeatedly through the same spots in its orbit on pretty much the same calendar dates each year. So in many cases, astronomers have mapped out the orbital paths of those old comets and can predict with varying degrees of accuracy when the Earth will experience a meteor shower. And because the orbital path of the shower is known, we can predict about what direction the shower will come from. -- further -- As the Question was asked on January 6th, I'm going to assume that it was prompted by a recent sighting. There are certain meteor showers which occur around this time Mid-December ...... The Geminids

Late-December...... The Ursids

Early-January......... The Quadrantids