1: Aesthetics. I like the look and feel of Civ 5's UI a hell of a lot more, and it has the best leader screens of any civ to date.
2: 1 UPT isn't perfect, but it edges out enormous stacks of doom by a slight margin IMO. "Ah, the Ottomans are slamming their 150 unit stack of doom into my city with 10 protective Longbowmen. Time to get a cup of tea." I also distinctly remember commonly retreating away from captured cities so I could use my city attack troops again to wipe out AI armies which would move back into the city. Rather ridiculous, but the best play nonetheless. Hardly ever was there a battle in the open field, which broke immersion for me.
3: Truly unique civ abilities. With the Iroquois, you don't chop forests. With the Netherlands, you will trade away even that last luxury, with Spain you will really try and find Natural Wonders to settle etc
4: Modding. Sure, Civ 4 has some immense large scale complete overhaul mods, but I found them to be poorly balanced at best (Except RFC. That mod was epic, I must admit). I myself am not a big fan of vox populi, but I loved Acken's Minimalisitc Balance and am currently really enjoying JFDLC, which really reminds me of RFC, come to think of it. Also, Civ 4 mods did not play well with eachother. You want this and that mod to work together? You'll have to combine them yourself. Acken's even makes the AI handle 1UPT perfectly, which is scary.
5: Almost no silliness. Civ 5 has no bobble head doll leaders, no Caesar's salad, no Gilgamesh jamming his face into the camera everytime he does not like a deal, Immortals aren't chariots, Rome builds Legions, not Praetorians.
Honorable mentions:
6: tech trading. By the time you advance through the difficulty levels in Civ 4, the goal for the human player is to research the techs the AI does not prioritize researching instead of researching the tech you really want, so you can trade that tech for many others. This made the game stale to me, because it made the tech path the same every game. Though Civ 5 has that problem to a certain extent as well (National College, I am looking at you), this is solved by almost every mod that's out there.
7: City states. I love these!
Funnily enough, I prefer Civ 5 over Civ 6. With Civ 6, I yearn back for stacks of doom because the civ 6 AI is literally (and yes, I do mean literally) incapable of taking an enemy city if it has walls. The aesthetics also do not fit my tastes. The civ 6 leader screens are too comical for me, and though I wasn't too opposed to the bright colours and more abstract shapes on the map on release, I have grown to dislike them over time. Hardly no penalties for going wide, which Civ 3, 4 and 5 all had, is also something that puzzles and annoys me.