After a night's sleep (men, troubled by the things they see in the night sky, toss and turn in their sleep... -- a play on the words of Loren Eiseley there 8>) ) it occurred to me that due to time dilation, light is ageless. Recall the example of a clock on a space ship slowing as the ship approaches the speed of light. At the speed of light, the clock comes to a standstill.
However, light telegraphs to us the apparent age of the cosmological event that was its origin, this by its observed doppler shift. So, I think the answer to your question is the light would not be 5.5 billion years old, but its observed doppler shift would not appear to be red-shifted as greatly if the solar system was traveling at 0.5c.
(Eyes roll back in head, need for more sleep is felt -- prepare for a ramble) This raises a hurdle that my simple mind has not yet overcome: With one or two nearby exceptions, all of the observable galaxies in our Universe exhibit red shift. In other words, regardless of the direction in which we look, all but the noted exceptions appear to be moving away from us. Paradoxically, that places us at the center of the red-shifting Universe with everything fleeing from us.
The gifted teachers of our times explain this phenomenon by pointing out that we can imagine our home galaxy and all others being on the surface of an expanding balloon. For a three dimensionally thinking person, this answers one question, but raises others.(p) What lies along the perpendiculars to the surface of or along the radii of the balloon inside and outside our "plane?" I found some relief in the pages of a book read back in the 1970s. I've forgotten its exact title, but I believe the author's name was "Kaufman" (or a variation on that spelling) and that he was employed at the Griffin Observatory in Los Angeles. In the book was an illustration divided into 4 sections by an "X". The intersection of the X was the "present." The area between the two top arms of the X was the "future." The area between the two bottom legs of the X was the "past." The two areas to the left and right of the present were "elsewhere." Perhaps the perpendiculars to the surface of our expanding balloon are elsewhere.