Hello!

I'll be telling you how to easily get rid of your intro videos safely.
This will only block the intro videos, the trailer videos can easily be disabled through the In-Game options menu.
It's actually fairly easy, although i'll still spread the process in multiple steps below.

1. Navigate to your CIV5 game folder.
(usually C://Program Files(86)steam/steamapps/common/Sid Meier's Civilization V

2. Delete/move/backup the following files:
- Civ5_Opening_Movie_de_DE.wmv
- Civ5_Opening_Movie_en_US.wmv
- Civ5_Opening_Movie_es_ES.wmv
- Civ5_Opening_Movie_fr_FR.wmv
- Civ5_Opening_Movie_it_IT.wmv

3. Head into the Assets/DLC/Expansion folder
(usually C://Program Files(86)steam/steamapps/common/Sid Meier's Civilization V/Assets/DLC/Expansion

4. Delete the following files:
- Civ5XP_Opening_Movie_de_DE.wma
- Civ5XP_Opening_Movie_en_US.wmv
- Civ5XP_Opening_Movie_es_ES.wma
- Civ5XP_Opening_Movie_fr_FR.wma
- Civ5XP_Opening_Movie_it_IT.wma
- Civ5XP_Opening_Movie_pl_PL.wma
- Civ5XP_Opening_Movie_ru_RU.wma

5. Now head over to the Assets/DLC map Expansion2
(usually C://Program Files(86)steam/steamapps/common/Sid Meier's Civilization V/Assets/DLC/Expansion2

6. Delete the following files:
- Civ5XP2_Opening_Movie_de_DE.wma
- Civ5XP2_Opening_Movie_en_US.wmv
- Civ5XP2_Opening_Movie_es_ES.wma
- Civ5XP2_Opening_Movie_fr_FR.wma
- Civ5XP2_Opening_Movie_it_IT.wma
- Civ5XP2_Opening_Movie_pl_PL.wma
- Civ5XP2_Opening_Movie_ru_RU.wma

7. Note
If in any case, you start missing your intro videos you can easily return the files(if backup) to their original location or verify the integrity of your game cache. (Right-click game title > propreties > verify integrity of game cache

8. Enjoy a quicker startup of Civilization 5!