I find 5E to be a good fit. 3E combat was far too stiff, with harsh movement options and "optimal" flanking positions. 4E combat as super fluid, but mostly because of forced movement (people still tried to get back to the "optimal" flanking positions). Also, IME 5E monsters drop far more quickly than either edition, so there is quite a bit of movement to face new enemies.
Some problems that keep 5E from being more fluid are actually perception based, rather than a system problem. Since you only take OA when you leave the enemies reach, you can move around enemies to get into a better position (such as to attack a different enemy). Most creatures don't do that much damage on an OA, so it's sometimes a good option to just take the potential hit (which opens up the move for others, since only 1 Reaction/Round). The withdraw action is usually underused, except by Rogues. Finally, Shove and Grappling can be used to force movement, they just don't also get to do damage (unlike most 4E forced movement attacks).
Some problems that keep 5E from being more fluid are actually perception based, rather than a system problem. Since you only take OA when you leave the enemies reach, you can move around enemies to get into a better position (such as to attack a different enemy). Most creatures don't do that much damage on an OA, so it's sometimes a good option to just take the potential hit (which opens up the move for others, since only 1 Reaction/Round). The withdraw action is usually underused, except by Rogues. Finally, Shove and Grappling can be used to force movement, they just don't also get to do damage (unlike most 4E forced movement attacks).
