Zyra was balanced last time for preseason 4. A suggestion to balance her for season 5
Zyra suffers as a midlane mage in from of mobility in contrast to other mages. I don´t say its not viable, but playing her in midlane became harder (every new champion got a displacement, Stalkers blade). Other Mages are easier to play, because they have either higher moventspeed or can buff their movementspeed with their kit (some champions can do even both).
A list of ranged mages and their mobility (of course there is e.g. Brand with 340 MS, but these are the most popular):
Ahri: 330 MS (+ Q + 3 dashes) Annie: 335 Azir: 335 MS ( + E) Cassiopeia: 335 (+ Q) LeBlanc: 335 (+ W + R) Lissandra: 325 (+ E) Morgana: 335 Orianna: 325 (+ W) Syndra: 330 Xerath 340
Zyra: 325
To be effective, Zyra needs to be close to her enemys (especially because of the short range of her ult). However, she is easily caught by any gap closer, if she is in cast range. Her only escapetool as a mage is her "E", which has quite a long cast animation (comparing to the kits of other mages) rooting Zyra longer in place additionally to her low movementspeed. And it doesn´t protect her from any kind of gabclosers.
I had the idea that we add a movementspeedbuff for Zyra, if her Vinelasher attacks an enemy champion. Her Grasping Roots does not benefit from additional cooldown if you max it. It stays at 12 seconds, so it couldnt be abused much in lane. I don´t believe that would be a huge buff on her as a support (it doesnt affect her laning very much unless you build early CDR, -> decision between Mpen rush and Cdr rush). Rushing Haunting guise with Sorc boots would give her still more survivability and effectivness, than a Morellonomicon with Boots of Speed.
But, this would effect her midlane. Zyra´s root is no displacement, she cant protect herself from J4´s ganks or Reksai´s for example, with their gap closers and knock ups. She is untouched since preseason 4 and i think this would be a small change bringing her up to date for Season 5.