This issue is most commonly seen on Windows XP, and may be caused by a bad video codec on your machine that prevents you from seeing the video or advancing to the game menu.
You may be able to resolve this issue by removing (deleting) the opening movie files from your game folder:
- For Civilization V, this file is typically located here: C:\Program Files\Steam\steamapps\common\Sid Meier's Civilization V\Civ5_Opening_Movie_en_US.wmv
- For Civilization V: Gods & Kings, that file is typically found here: C:\Program Files\Steam\steamapps\common\Sid Meier's Civilization V\assets\DLC\Expansion\Civ5XP_Opening_Movie_en_US.wmv