That’s not how it works. You’re correct when you say that from your point of view it’s Earth’s clock going half speed and from Earth’s point of view it’s your clock going half speed while you’re traveling away from Earth (or Earth is traveling away from you, both are equally valid), but that’s only true as long as the distance between you and Earth continues to increase at 86% of the speed of light. As you decelerate at your destination your reference frame continuously changes until you’re back in the same frame as Earth (or nearly so, we can assume the two stars aren’t exactly maintaining their relative positions). While you’re decelerating, from your perspective Earth’s clock speeds up, how much is determined by your rate of change in relative velocity. Earth’s reference frame isn’t changing (ignoring movement around the sun, galactic center, the great attractor, etc.), so the Earth’s perspective on your clock doesn’t change. So once you’re back in the Earth’s reference frame both you and the Earth will agree that your clock advanced 5 years while Earth’s clock (and your destination’s clock, adjusted for any relative movement between it and Earth) advanced 10 years. This assumes a constant 86% light speed and ignores the time accelerating at departure and arrival so let’s assume very fast acceleration so it doesn’t change more than a couple days.
That’s not how it works. You’re correct when you say that from your point of view it’s Earth’s clock going half speed and from Earth’s point of view it’s your clock going half speed while you’re traveling away from Earth (or Earth is traveling away from you, both are equally valid), but that’s only true as long as the distance between you and Earth continues to increase at 86% of the speed of light. As you decelerate at your destination your reference frame continuously changes until you’re back in the same frame as Earth (or nearly so, we can assume the two stars aren’t exactly maintaining their relative positions). While you’re decelerating, from your perspective Earth’s clock speeds up, how much is determined by your rate of change in relative velocity. Earth’s reference frame isn’t changing (ignoring movement around the sun, galactic center, the great attractor, etc.), so the Earth’s perspective on your clock doesn’t change. So once you’re back in the Earth’s reference frame both you and the Earth will agree that your clock advanced 5 years while Earth’s clock (and your destination’s clock, adjusted for any relative movement between it and Earth) advanced 10 years. This assumes a constant 86% light speed and ignores the time accelerating at departure and arrival so let’s assume very fast acceleration so it doesn’t change more than a couple days.