There seems to be a lot of confusion as to what reboot means, as far as I can tell from these posts.
Here's my take on it, for what it's worth: A reboot is essentially a retelling of a classic story franchise. It doesn't have to borrow the exact details of the plot, even. Many episodes or movies have basic parts that you can swap out and still maintain the structure of the story (hero, villain, love interest, plot-twist, etc). What's important is that you have enough elements from a series to make it somewhat recognizable. So the new Star Trek has Kirk and Bones and Spock in it, even though the story itself is "original," in the sense that isn't an exact retelling of an old episode or film from the franchise. It is something "old" that has been adapted to modern audiences.
So, simply put, a reboot is an adaptation. It's Mary Shelley's Frankenstein, the novel, versus Kenneth Branagh's film of the same name. It's Star Trek the 1960's TV show versus the 2009 J.J. Abrams film of the same name, and so on.
A sequel, on the other hand, is a continuation of a story or episode. It is Empire Strikes Back following A New Hope. It is The Fly 2 following The Fly. The stories are actually connected, and more than thematically. They are sequential and take place in the same universe, with the same exact characters, and are distinguished from one another chronologically.
Alien 5 is a sequel because it takes place in the same exact universe that Cameron created, with the same characters, following the events that transpired in Aliens, just as Aliens was a sequel for the same reasons in regards to Alien.
That's how I see it, anyways.