Why doesn't my iPod touch (5th Gen) have FaceTime?
You should at least see a FaceTime icon in Settings:



If you don't, FaceTime may not available in your country. According to Wikipedia and Apple these countries don't support FaceTime:


Saudi Arabia
United Arab Emirates 
Pakistan


If that's not your case, please check this document. It explains what to do to troubleshoot a missing FaceTime app. This is the relevant section:


Note that FaceTime may not be available on devices purchased or used in certain countries, including Saudi Arabia and the United Arab Emirates.
In Settings > General > Restrictions, verify FaceTime and Camera are On. 
Disabling Camera also disables FaceTime.
Update to the latest version of iOS.
Restore your device:


Back up your device to iCloud or iTunes.
Tap Settings > General > Reset > Erase All Content and Settings.
Note: This will erase all user data from your device.
When complete, configure your device by selecting your region and language and then restore your data using the iCloud or iTunes backup.
Note: When setting up and restoring a backup from iTunes, ensure that your computer's language, country, and date and time are set correctly.

If you still cannot locate the FaceTime app, try turning it on at Settings > FaceTime.