I'm using LR 5 on a Mac (10.9.5).
Importing video clips into LR 5, it automatically flips them vertically. I checked the original video's with Quicktime and other media players and it oriented correctly. iMovie also shows them correct. As soon as I import the video in LR it flips them vertically and there is no way to flip them back in LR.
What can I do to get the videos show correctly in LR 5?
Please check that you not selected any develop preset while importing the videos in Lightroom.
If its already selected as "None", then try creating a new catalog and import some video file and check if that helps.