Quote from Tatsu;136340:
Aren't supernatural/magic pretty much on the same side of the coin?
Not really, they're similar but they're different. Magic would be more like... well magic. You know, glowy circles, spell casting, etc. Supernatural can be something like powers which may resemble Magic but isn't, things like the Death Note, Geass, Vampires, etc. Horror also tends to fall into Supernatural because of things like ghosts, demons, etc.
Anyways...
I searched MAL's database and theres only 1 anime that has all 5 genres. Asagiri no Miko. I've never even heard of it before so I can't say much. It's pretty much impossible to find a decent anime with all 3 Sci Fi, Supernatural and Magic in it.
I typed down a crap load but then my browser just closed on me after typing like 1000+ words of short descriptions and titles. I raged. Now I'm only gonna type titles. Most are shounen, it's fairly impossible to find a shoujo without romance/drama as the main genre and drama/romance wasn't in the genre request so I'm ignoring it, some might have the two but I do not think any of what I listed are Shojo's. Also, I'm not sure what you've seen so I just named whatever... in alphabetical order.
Asu no Yoichi!
Black Cat
Busou Renkin
Baka to Test no Shoukanjuu
Chrome Shelled Regios
Elemental Gelade
Eureka Seven
Fate/Stay Night
Gintama
Hunter x Hunter
Kaze no Stigma
Mai-HiME
Matantei Loki Ragnarok
Needless
Night Wizard
Rental Magica
Pandora Hearts
Seiken no Blacksmith
Shining Tears X Wind
Tales of Abyss
The Law of Ueki
Tokyo Majin Gakuen Kenpucho
Tokyo Underground
Tower of Druaga
Yokuwakaru Gendaimahou
I'm forgetting a lot.