The system is 11.2 billion years old and was born near the dawn of the galaxy, said the report in the Astrophysical Journal.
The star has been named Kepler-444, since it was found with the help of NASA's planet-hunting Kepler spacecraft.
Its five planets are a bit smaller than the Earth. They circle their Sun-like star in less than 10 days, at a distance smaller than one-tenth the distance between the Earth and Sun -- making them too hot to be habitable.
At a distance of 117 light-years from Earth, Kepler-444 is two and a half times older than our solar system, which is 4.5 billion years old.
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"We've never seen anything like this -- it is such an old star and the large number of small planets make it very special," said co-author Daniel Huber from the University of Sydney's School of Physics.
"It is extraordinary that such an ancient system of terrestrial-sized planets formed when the universe was just starting out, at a fifth its current age," he added.
Astronomers can measure a distant planet's age using a technique called asteroseismology, which measures the oscillations of the host star caused by sound waves trapped within it.
Co-author Steve Kawaler, an Iowa State University professor of physics and astronomy, said Kepler-444 is very bright and can be easily seen with binoculars.
"We now know that Earth-size planets have formed throughout most of the universe's 13.8-billion-year history," said lead author Tiago Campante from the University of Birmingham.