I read this is a very common problem and no, it isnt Instagram app error but ROM fault as many Nexus5/other phones can upload videos (read in internet)
follow these steps to prepare your video:
- Record your favourite video with you camera, MAX ALLOWED TIME 15s for Instagram
- Instagram accepts only two sizes: 480x480 - 680x680. If it is bigger it will zoom it in center to fit it needs, so take it in account when editing video, for example i recorded a full hd video with my S3 and then i edited it to 720x720 adding black borders.
- Rotate your video 90° degrees anti-clockwise (Instagram seems to rotate video on upload)
- MP4 video format
time to open Instagram! :
- Open Instagram app
- Record about 20s of video
- Press HOME button, leaving Instagram app opened in background
- Go to sdcard/Android/data/com.instagram.android/files/video/random_named_folder/your_just_recorded_video.mp4 - that's the folder where Instagram save your just recorded video
- Copy in this folder your video you want to upload
- Rename your video with the Instagram created one and then delete Instagram video
- Resume from background Instagram
- Press right upper corner blue arrow and then you'll see your video in preview!!
Some side notes: On OmniROM it doesnt work, everytime Instagram crashes, so you have to use another/stock rom. I used FreeMake "Free Video Converter" to adapt my S3 full hd video to Instagram format. I first made it 15s long by selecting only part i wanted to upload. Then i created under Convert->Android label a new custom profile with: MP4 - 720x720 - Cropping style: Original - other fields default. Then i converted my video and did steps i just wrote. If you dont like Instagram video preview just play a bit with resolution/cropping way in Video Converter, i just wrote what i used
higher video bitrate will produce better quality and bigger videos, i tried with 8000 Kbps and it works, however Instagram will take more time to process your video!
At least we have a working way until rom devs fix your current rom
This tut can also be used for Vine and other phones/tablets/ROMs !!