All this "4E fights took forever" talk is strange to me, because fights in D&D have always taken a long time for my group, especially at higher levels. Spells, tactics, multiple monsters, maps. We rarely have "easy" or "medium" fights because we like the challenge of the harder fights.
The last boss fight we did in my 5E game took 12 rounds, and two of the enemies got away. There were 3 leveled NPCs and 2 hill giants, and the party of 5 had 9 NPCs on their side helping. Big climax of a city siege.
The dragon fight earlier took 6 rounds, and the cleric's turn often takes a while (the warlock is faster), and the fighter can even take a bit if he's using his superiority dice that round.