I'm just about to wrap up my first level 1-20 campaign for 5E. I also have multiple active lower level campaigns. After over 150 sessions, I feel like I have a solid grasp of how the game plays. Here's the headline: 5E plays just fine at all levels.
At 20th level, I can run monsters straight out of the book against player characters built straight out of the book. PCs are very powerful but not invulnerable. Combat is a bit slow and grindy. However, I have five PCs plus allied NPCs, so our sessions have always been somewhat slow. But it's not enough to kill the tension and I can still generate suspense.
One recurring point of friction is between short rest classes vs long rest classes. My group rarely takes shorts rests, in part because I like to put them on a ticking clock. The result is that short rest classes have felt underpowered. I've tweaked the rules to accommodate that, but it came late.
Monster design is also simply not as elegant or exciting as 4E. Related to that, I wish that 5E had taken 13th Age's approach to building dynamic combats without the requirement of a grid. 5E is distinctly tilted more toward an attrition model than a set piece encounter model -- and I prefer the latter as it supports more cinematic storytelling.
Overall, 5E has been a great D&D experience.