Is it Impossible to transfer videos from an iPhone 5 to an iPad 2?

Well, is it?

No, you can get an iCloud account. It allows you to share videos, music, etc.between all of your apple devices.

It's not "impossible" in fact it's very likely to transfer pictures and videos from a iPhone 5 to a iPad 2 or any other apple device. All you have to do is connect your apple device to your computer (like a USB stick, but for this you'll need a apple USB adapter this comes with your device) next once your device is plugged in and running on your computer go to start > computer > and look for your device name > and keep going through the files until you see the pictures. Once you see the pictures or videos you can copy them as in right click. And than plug your other apple device like for example an iPad 2 you can plug that in now and follow the same process start > computer > and look for your device name > and keep going through the files until you see the pictures… Now you can paste the pictures or videos you copied from the other device and now your done… You can turn on your device while plugging it out from your computer and check to see if your pictures are there.

You can make use use of Wi-Fi network to transfer videos from iPhone 5 to iPad 2. If you choose the appropriate app, there's no need of iTunes, computer, and usb cables.
http://www.iphone-photo-transfer.com/

Generally speaking, no, but with iPad Manager Platinum from 4Videosoft Studio, you can easily transfer videos from an iPhone 5 to an iPad 2.it helps me transfer files from iPhone to iPad. It's a great app, you can Google it and have a free try.