That's a combination of misleading and outright false. What's misleading is you're suggesting that iCloud Backup and Photo Stream are doing redundant work. While it's true that both involve uploading your photos, Photo Stream only keeps the last 30 days (or 1000 photos), whereas iCloud Backup is a complete backup of everything. It must include your complete photo library, even the photos that are currently in Photo Stream, because there's no guarantee that the photos will still be available in Photo Stream when you decide to restore.
And what's completely wrong is your assertion that iCloud Photo Library is including redundant information yet again. This is wrong because if you enable iCloud Photo Library, then your iCloud Backup stops including the camera roll. If you have both iCloud Photo Library and Photo Stream enabled, I hope it only uploads the photo once, but I haven't done any measurements.
So no, this does not "turn 5GB of pictures into 15GB". It's not even 10GB (1000 photos is significantly less than 5GB).