UnCiv covers civ 5 as well so I think there's a place for something in between
replyespecially since openciv3 aims to fix some of civ 3's shortcomings
Til! I should give UnCiv a try, I've sunk a lot of hours into 5 but didn't know about this.
replyFreeciv's point of interest is that it's not trying to exactly replicate any one of the original Civs: it has its default ruleset plus others that are closer to the original games, but it's very easy to make your own.
replyWhich FreeCiv? The one you install locally, or the one you play via browser on the Web?
replyThe latter has more, like Multiplayer 2.4 Dragoon, and Multiplayer 2.5 Elephant(in development), which weren't available locally when I last looked.
There is also https://github.com/longturn/freeciv21 which has an acceptable local client, and finally does not slow down so much when playing larger maps with many AIs, like both FreeCiv and FreeCivWeb tend to do.
https://longturn.readthedocs.io/en/latest/index.html
I tried that, recently, and barely espcaped a relapse. (Phew!)