Before I explain my idea, let me state that I have no clue what virtually any existing Alien-5 scripts happen to describe. Any similarities are mere coincidences. What I am basing this off is largely some early theories the '79 writers and directors had about the biology of the xenomorph.
The film would start off with a brand new crew in space, descending on a brand new planet. This planet is years and years away from earth, even travelling beyond light-speed. It has never been explored before. The crew aboard the ship is a scientific exploration team.
After landing and exploring, one of the crew members gets face-hugged and gives birth to a Big Chap Xeno. The crew manages, in some way, to kill the alien. This all happens rather quickly. But once the alien is dead, the ship is surrounded by dozens and dozens more Xenos, which basically destroy and conquer everything and everyone. The only catch is, the exploration team had already sent a distress call back to earth.
Back on earth, and much time later, Ripley-8 is living by herself. She is divorced, has had children, and grandchildren. But everyone, including her offspring, has disowned her due to her fascination with bizarre things, particularly the Xenomorph. One day she gets a transmission – that the exploration team had encountered Xenomorphs living on another planet, and had been dismantled and conquered by them.
Ripley-8 100%, off the bat, agrees to travel to the planet with a space squad of thousands of marines, to battle the Xenomorphs. But when they arrive, they find something no one would ever expect:
There are millions of Xenomorphs living on the planet, and the ones more than a couple years old have gone through a metamorphosis of some kind. They have become intelligent, and cultured... and look different, as well.
Most of the space marines are killed. Despite their intelligence, the Xenomorphs still want to breed, and conquer. A few of the marines, including Ripley-8, manage to retreat, hide, and plan. Their ship is destroyed, however. But they do find a very small group of the first humans who arrived earlier in the film, who have been living there on the planet all this time (not sure how they managed to survive, though – use your own imagination to come up with ideas!).
Not only are the new Xenos more intelligent and cultured than humans, they have adapted their culture to mimic the culture of the first humans who arrived, as well as many other cultures whom they've colonized. At some point they explain their plans to conquer as much of the visible universe as possible.
Now – this is where it might get a bit messy and blurry. I'm not totally sure where to go from here. But what I envision is one of Ripley-8's children, who had been trailing her ship, arriving on the planet and basically telling Ripley-8 to "Grow up, mom", that she's reckless, etc. Ripley-8's child has come to stop her from endangering earth, something that her son/daughter blames her for doing in some way all along.
Upon being slandered by her offspring, yet again, a powerful plot-twist happens – Ripley-8 loses it and joins the Xenomorpths, who gladly accept her due to being part alien herself. Ripley-8 destroys all the humans, and at the end of the film, takes off in a space-craft UFO built by the xenomorphs so they can conquer more of the universe – starting with EARTH.
What I picture is Ripley-8's child (Adult son or daughter) managing to survive the final battle with one or two other humans, and whispering "We're gonna get her".
PS: One issue I'm having is with how this new planet got infested with Xenomorphs in the first place. But I think it's rather moot. I don't remember much of Alien: Covenant (and I'm glad!). Nor do I care to. I couldn't care less about those movies, so it doesn't matter to me even if they contradict any of this Alien-5 idea. I envision that the Xenos are are species that has been around for hundreds, thousands, or even millions of years. The Space Jockeys seen in the '79 film were not the "beginning" of the Xenomorph, so anything LV-426-related just doesn't matter.
What the ending of this film would do, is pave the way for an Alien-6 movie with the Xenomorphs arriving to colonize earth, now that they not only know of earth's existence, but they also have their saviour, their prophesied Messiah – Ripley-8 with them. She could now be the villain in the Alien-6 film, and possibly after.