Assume I travel near c from a planet 5 light years away

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to the earth. I will arrive at Earth a little over 5 years from the time I depart, correct? How many years will I have aged as a passenger on the spaceship and how long will someone on Earth have aged during my journey?
 
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According to an observer on the Earth, your journey took a little more than five years.

According to you, aboard the spaceship, your journey was nearly instantaneous, and you would have scarcely aged at all.

- Warren
 
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