Opportunity attacks are a big simplification in 5e too, as well as the other points that people here mention. Basically you only trigger an OA when you leave the reach of an opponent without using the withdraw action. That's it. No OA from casting in melee, or taking something out of your backpack, or using a bow up close, or standing up from prone. Those things usually use disadvantage.
Another thing that came up in our group last session was the rogue getting sneak attacks using his dagger when our cleric was standing alone in front of a hobgoblin. It's much easier to get SA in 5e at range, which makes rogues a bit more versatile and was one of the big complaints about 3.x rogues. The player of the cleric didn't believe that rogues could SA from afar, and the DM wasn't aware either. We're all fairly experienced players but that's why you really should not assume that anything works the way you think it does. There will be surprises, even after you've been playing the game for a while. Fortunately it's not a big deal to make mistakes and use d20-isms until you unlearn what you have learned.

There are lots of little nuances that come up that eventually you will see are simply better in 5e. A couple are worse, but no system is perfect.
Combat is really dynamic because you can move-attack-move (-attack-move-attack-etc as long as you have extra attacks and/or movement left). And you don't trigger OAs if you run circles around your opponent but stay within their reach. It's really nice and part of what makes the system great. It's a fine bit of engineering, and a job well done.
Once you play 5e you'll realize that what at first appears as though it's quite simpler, in practice combat is a lot more fun, dynamic, balanced (vs casters) and melee types aren't slaves to "full attacking". The game is just better than d20 in pretty much every way. It's also more old school, and the simulationism it does have is elegant and not falling into the side of tedium and annoyance.
I agree with what others have said about adv / disadv. It's a massive time saver to avoid all these little bonuses and penalties. And I'm very happy that annoyances like two weapon fighting penalties are gone. The BAB weapon attack staircase is also gone, meaning all your attacks are at the same bonus. Plus the numbers are much smaller.
It's easily the most mechanically sound D&D yet, try it you will see. It will be hard going back to d20 afterwards. I refuse to play any non-5e game now, even in campaigns that started in 2e / 3e / 4e. It's easy to migrate them over and require a lot less work. Also it's really easy to DM, that's one of the big benefits. The rules are streamlined and logical, for the most part. Yeah, a great game system.
Cool. cool,cool,cool