This question is known as "Olbers' Paradox" after the scientist who first posed it, back in 1823.
The point of the paradox is that if the Universe is infinite, that would mean that if you go far enough in every single direction, you would eventually hit the surface of a star. Therefore, the night sky should be bright, not dark.
The answer to the paradox is that the Universe is not infinite in space-time. At the time of the Big Bang, 14 billion years ago, it was very small, and it has been expanding ever since that time. That means that we cannot see anything that is over 14 billion light-years away, because there has not been enough time for its light to reach us yet.
And by the way -- with any pair of binoculars, even a bad pair, you can see more than 5000 stars with your own eyes.
And I hope someday you can get online and IM with somebody in Australia. If you do, be sure and ask them if the Sun is up where they are.