It would take only 12 years to reach the planets when travelling at the speed of light.
Scientists analysing about 6000 measurements of the star Tau Ceti's velocity, believe that slight inconsistencies in its speed and direction are being caused by the gravitational pull of other celestial bodies, The Australian reported.
"We believe the star is going very slightly backwards and forwards and shows the evidence for doing that at five different periods," said Professor Chris Tinney of the University of New South Wales.
"We think five different planets are going around that star tugging on it making it move backwards and forwards," Tinney told AAP news agency.
An international team of researchers from Australia, Chile, the United Kingdom and the United States believe one of the five planets orbiting Tau Ceti is within the star's habitable zone, where conditions are suitable for life.
The planet in the habitable zone has a mass about five times that of Earth, making it the smallest known planet orbiting in the "Goldilocks" zone - where conditions are just right - of any Sun-like star.
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Tinney said scientists believe smaller, rocky planets have the best chance of hosting life.
The finding comes after 14 years of research and analysis, and it might take that long again before scientists are certain of what lurks in Tau Ceti's neighbourhood.
"But if somebody else could prove that we're wrong, I'd be more than happy with that," Tinney said.
The planets, of which the smallest is at least twice the size of Earth, are too far away to send probes to explore.
"Even if we could send something at the speed of light, it would take 12 years to get there and 12 years to send a signal back," Tinney said.
"At the moment we have no way of even getting close to a 10th of the speed of light," Tinney added.