Does your Aperture version support Shared Photo Streams? You can transfer videos by sharing them to a shared photo stream, see:
- iPhone, iPad, or iPod touch with iOS 7.0 or later
- Mac with OS X Mavericks v10.9 or later and either iPhoto 9.5 or Aperture 3.5
- AppleTV (second generation) with Apple TV software 6.0 or later
- PC with Windows 7 or later and iCloud Control Panel 3.0 or later
If the owner of the shared stream has turned on the Public Website option and shares the link with you, you can use any up-to-date browser to see photos and videos added by the owner and all contributors.
Another way to upload videos to your iPhone would be to sync them using iTunes. You would have to import the videos to your iTunes library and set up iTunes to sync movies.
I don't use shared streams....I have over 10 GB of videos taken and it will take forever to sync....
That's why it's a bummer that you can't sync videos taken with your phone back to it.
You can export it to iTunes but the thing with the new iPhone 5S videos is that you loose the slow motion adjustability.