How do I transfer mp4 videos to my iPhone 5 through iTunes?

Hello User90080,

First you would need to add the file to iTunes if its compatible:

To add files to your iTunes library, you can use these options:

• Drag files from the Finder to the appropriate icon on the left side of the iTunes window.
• Choose File > Add to Library (on Windows, choose Add File to Library or Add Folder to Library) and select the song or folder that you want to add.

iTunes adds entries to your iTunes library for the selected files and copies the files to your iTunes Music folder (if you selected that option in the Advanced pane of iTunes preferences).

From: iTunes: About the Add to Library, Import, and Convert functions

http://support.apple.com/kb/ht1347

Then you should be able to use iTunes to sync it to your device.

USB syncing

1. Open iTunes.
2. Connect the iOS device to your computer using the included USB cable and click the device button in the upper right corner. (If you are viewing the iTunes Store, click the Library button in the upper right corner. The device button will then be visible.) Some tabs may not appear if you do not have corresponding content in your library. For example if you do not have any podcasts in your library, the corresponding Podcasts tab will not appear.
   
3. You can configure the different content types in each tab. For example, movies under the Movies tab.
4. To sync, click Apply, in the lower-right corner of the screen.

Note: If the iOS device does not appear in the Devices section or if you are unable to sync, please follow these troubleshooting steps.

From: iOS: How to transfer or sync content to your computer

http://support.apple.com/kb/ht1296

Thank you for using Apple Support Communities.

All the best,

Sterling