D&D5 has replaced most of these nitpicky bonuses and penalties with advantage and disadvantage. For advantage and disadvantage, the rule is simple. You roll two twenty sided dice instead of one. If you have advantage, then you pick the better one. If you have disadvantage, you pick the worse one. If you have things that grant both advantage and disadvantage, you roll as normal.
This development simplifies a lot of things and while I could definitely have talked about this in relation to my first point about randomness, I think this has the most potential impact when it comes to running games. No longer do you have to pore over books to find what the balanced level of benefit or penalty for a given situation is, you can instead simply give advantage or disadvantage based on a given change in circumstances.
One of the biggest problems with D&D has always been that it's been hard to justify situational modifiers because of the strictly balanced set of bonuses and penalties at the heart of the game. The addition of advantage and disadvantage changes that. And what's great is that advantage doesn't let character exceed their current ability, it just smooths out the bell curve of success, making them less likely to fail.