Skim through this thread for a general idea:
http://forums.civfanatics.com/showthread.php?t=470659
The link in that OP is broken, here is the fixed link (click on "View Raw" to download it):
https://github.com/malkia/ufo/blob/master/bin/Windows/x86/luajit.dll
1) Navigate to Steam\steamapps\common\sid meier's civilization v\
2) Find the file: lua51_win32.dll
3) Delete or rename this file.
4) Add the new .dll file that you downloaded into this same folder and name it the exact same thing as the old dll: lua51_win32.dll
5) Play the game. If you get crashes, you probably did something wrong.
Optional: Copy and backup the original .dll somewhere on your computer. It's optional because you can always just delete what .dll you have in the folder and then have Steam verify game cache to redownload whatever files are missing.
The wait between turns had me so frustrated that I stopped playing Civ V for a while and went back to IV. Then I tried out using that new luajit.dll (you need to rename it as it says in the thread) and now the time between turns is ridiculously fast.
Caveat: This new lua engine breaks a lot (most?) mods since they were written with the game's original lua scripting in mind. Stuff like CivUP or Cultural Diffusion won't work anymore, but stuff like Colored Religion Icons or other "simple" mods will work just fine.
I've been using this LUA engine for months now on Win 8 64-bit and previously on Win 7 64-bit. Been playing the game on DX10/11 the entire time as well.