The answer to this question really does have a big matter of opinion ascribed to it. I'll give mine and try to stay objective. The other answers/comments were only recommending to watch the first two, but I would not, so I think people will miss out!
The 5 movies in order (whether recommended or not) are:
- The Terminator (1984)
- Terminator 2: Judgment Day (1991)
- Terminator 3: Rise of the Machines (2003)
- Terminator Salvation (2009)
- Terminator Genisys (2015)
There are also two seasons of
The Sarah Connor Chronicles (2008-2009). I can't speak to that, because I only got ~10 minutes into the pilot before I gave up on it. If I give it another try I'll come back here and give more information. (Top commenter on IMDB: "Trust me, the people giving it bad reviews watched only the pilot or two episodes and gave up too quickly. The show evolves and gets much better than the first few episodes.")
Short answer: definitely watch
#3. Probably watch
#4 and very-maybe watch
#5 (read on for more). Note that this answer is for the actual question (what to watch prior to
#5) and also just what to watch in general.
You could consider
#2 to be the classics. You kinda have to watch them, but fortunately they're (mostly) a fun watch anyways, even for their creation date.
#3 does a pretty good job of fitting in with the prior storylines, has an even cooler terminator, and yet still manages to make good use of Schwarzenegger's terminator.
#4 is a little different and doesn't have Schwarzenegger; but, I still highly recommend it. You could think of this one as being like
Rogue One (from the
Star Wars series) or
Logan (from the
X-Men series) but for
Terminator; as someone said above, it doesn't add much to the storyline, except that instead of cyborgs, men are now being used to make infiltrator-robots. It kind of has elements from
War of the Worlds,
iRobot mixed in. (Also, it took me a while to realize that there were two main characters, which was confusing, as they kind of look alike and it shifts from one character's story to the other's early on in the movie, so watch for that.)
#5 is a total timeline mix-up and is entertaining but only recommended if you're into that sort of thing. It has different characters for Kyle Reese, Sarah Connor, and John Connor (even from
#4), but it does manage to bring Schwarzenegger back into it (and he definitely fits in well and brings back the old
Terminator theme). It's pretty obvious that the goal in mind was to go full-blown alternate-timeline for the entire movie, kind of like a
Back to the Future movie, except not as excellently. Between that and the different characters, this is why some may not like
#5. It wasn't as enjoyable as the prior 4 due to its different characters and all of the randomness going on in order to make the alternate timeline seem really cool, but it still had some entertainment value and may be worth the watch.
Lastly, note that
#1 has two really long, uncomfortable sex scenes (with some nudity), and the rest of the movies all have a bit of nudity (
#3 especially, in one of the first scenes) - but those instances are mostly brief/non-sexual.