HOW TO MAKE THE GAME LAUNCH IN WINDOWS 10.

Well, I don't really know, but it can happen any time you are playing in Windows 10, even if the game used to run fine before, and consists in the game just don't launching after clicking "Play".

This is a guide to solving it PERMANENTLY so you can play Civ 5 in Windows 10.

Well, this is a little tricky, first of all, you need to follow this steps I found after digging very deep in a discussion about the problem:

1 - Open the game in "legacy beta", using the beta code "ineedlegacyaccess". This is an old version of the game from before the 2K launcher was added.

2 - Paste this in your launch parameters:
"D or C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization V\CivilizationV_DX11.exe" -dxlevel90

3 - Go to C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization V and launch the launcher.exe in the folder.
You see it bypass the “Updating Executable” this time and start installing some Directx files (you can see this in your Steam client next to the play button at the moment you use the launcher.exe from the game folder.

4 - When this process is done once you can simply delete all launch parameters and run the game normally as always. There is no need to change read/write rights or to change admin rights this way.

With all of that, you should be able to play the game just fine. At least this was the only thing that solved the problem for me. Credits to @Cablenexus for giving the step-by-step.