TL;DR version: It's disappointing. There's more to it than that, though.
I've read a lot of reviews and reactions, both glowing and scathing, and am surprised to find that I disagree with pretty much all of them. IMHO, the action scenes and special effects were top notch, there were some genuinely funny moments, Arnold Schwarzenegger and Emilia Clarke did a great job, the recreation of 1984 was beautifully done, and the future war scene in the beginning - despite some forced dialogue - was a joy to watch. I wish we'd gotten to see more of the actual battle. They tweaked the T-800 endoskeleton design, but we barely got a good look at the new chassis.
I've imagined the events immediately surrounding Kyle Reese getting sent back in time for over 30 years. Finally getting to see it got me a little misty.
However, the story was an unmitigated mess. The "memories from an alternate timeline" idea insulted the audience's intelligence, Genisys-as-tablet-app-that-also-has-acce
I don't regret having seen it three times. There are some very cool things about the movie, and many absolute atrocities. I'm reading the behind-the-scenes book ("Resetting the Future") now, and it's really interesting. Despite my overall negative opinion, I genuinely hope the movie does well enough to warrant two more in the series. I'd like them to have an opportunity to explain some of the unanswered questions. The writers apparently have the entire story arc plotted out. If the next two movies don't happen, I hope that they'll at least give us the rest of the story in some other medium. The Terminator Salvation story got truncated. It'd be a shame to have that happen again.
Either way, the Cinema Sins review is going to be a hoot!