The movie did ok at the box office, better worldwide, but not enough to be fast-tracked by Paramount for sequels, which nonetheless may be still be made. It was panned by many critics. I had lots of problems with it, but also thought it had some redeeming elements. I loved the first two Terminator movies, the third almost as much, and enjoyed the fourth (though a lot of people didn't - enjoy the fourth, that is). I also enjoyed and reviewed the television series. See the links below. All told, given this history and the bright parts of Genisys, I'd definitely like to see more sequels.
Here's what wasn't so hot in the movie: A lot of the dialog is ridiculous, such as Sarah Connor saying "bite me". A lot of the acting - including Emilia Clarke from Game of Thrones playing Sarah - was nothing special, either. She was no Linda Hamilton or Lena Headey (TV series) in the role.
Here's what I liked: Arnold Schwarzenegger reprising his Terminator role, in fact as a young, middle-aged, and old version of him/itself. He did this with just the right mix of seriousness, wooden style, and humor - including a smile he is trying to convey, to make himself seem more human, but which only makes him more frightening, right in the uncanny valley. The plot around this Terminator is good, too.
And the same for the overall storyline. There's respect for paradoxes of travel to the past, attempts to explain how someone could remember a history which his or her action had eliminated, and some good twists regarding heroes and villains. And the Genisys being Skynet, drawing a connection between our social media giants and the emergence of Skynet, was a nice touch, too.
J. K. Simmons also was excellent as an older detective who had an encounter with our heroes when he was a young cop, and Jason Clarke as John Connor was pretty good, too.
So, yeah, I'm down for another movie or two or more. Emilia Clarke says she won't be back - sorry, but she's much better in Game of Thrones. Our growing 24/7 immersion in social media - which I actually think is mostly a good thing - makes the Skynet story, especially now as Genisys, more relevant than ever. Hey, maybe my enjoyment of social media is part of the very problem that made our species so vulnerable to Skynet. But I'm not worried - as long as there's a good Arnold-Terminator model on hand to help us out.
See also Terminator Salvation: A Compelling Time Travel Story Nonetheless
and also my reviews of The Sarah Connor Chronicles 2.1 Cameron's Back ... 2.2 Firing on All Cylinders ... 2.3 Who, Truly, Is Agent Ellison? ... 2.4: Meet Allison ... 2.5: Unpacking the Future ... 2.6: Terminator Mom, Human Daughter ... 2.7: The Saving Robbery and Cromartie ... 2.8 Perspectives and Death ... 2.9: An Idiot's Guide to Time Travel in The Sarah Connor Chronicles ... 2.10: Riley Lashes Out at Facebook ... 2.11: Cameron Meets A. E. Housman and Andre Bazin ... 2.12 Sarah Connor Chronicles in Triple Time ... 2.13: Space, Time, and Blogging in The Sarah Connor Chronicles ... 2.18: The Sarah Connor Chronicles and the Life of Riley ... 2.20: Sarah Connor vs. Death in Two Forms ... 2.21: Profound Lessons from a Kidnapping in The Sarah Connor Chronicles ... The Sarah Connor Chronicles Season 2 Finale
And from Season 1: The Sarah Connor Chronicles 1 and 2 ... 3 ... 4. A Robot Primer ... 5 ... 6 ... 7 ... 8-9
time traveling a little further back in history ...