It has always been my understanding that under E=MC2, an object leaving earth traveling at .999 C would cover 5 light years in approximately 5 years while the relativity effect would result in many more than 5 years passing on Earth. In other words time for the light speed traveler would be normal but the elapsed time at the origin and destination would be dilated.

I have recently read a couple of scifi novels where the reverse is true. The 5 light year journey would only be a few weeks for the traveler while the elapsed time at the origin and destination would be the normal 5 years.

Which is correct? I understand that near light speed is not attainable due to the infinite energy requirement but in theory how does the time dilation thing work and can the time differential be calculated.