According Wikipedia on the topic of Wu Xing, which is the source of the five elements you listed, here is what falls under each school:
Wood (New Yang): Wind, Moisture, Air, Minerals, Mana, Ink, Mind, Rubber, Paper, Plants, Poison, Wax, Dissolve, Carbon, Clouds
Fire (Full Yang): Heat, Light, Lava, Radiation, Sparks, Plasma, Explosions, Burn, Blaze, Oil, Ash, Smoke, Glass, Napalm, Sun
Earth (Yin/Yang Balance): Clay, Rock, Dust, Sand, Mud, Crystal, Powder, Shadow, Space, Darkness, Gravity, Bone, Quake, Silicon
Metal (New Yin): Lightning, Magnetism, Electric, Rust, Gold, Silver, Steel, Iron, Platinum, Titanium, Copper, Bronze, Brass, Blood, Forge, Stars, Diamond
Water (Full Yin): Sea, Ice, Storms, Rain, Steam, Fluid, Sound, Mist, Acid, Slime, Salt, Time, Pressure, Moon
I'm going to be fairly loose with these definitions, I'll admit. So, for the Animari, biological transformation likely falls under Earth, which contains "bone" and also "clay," which could count for shaping bodies, although "blood" and "forge" from Metal could be equally useful, simply in a different capacity. Perhaps Earth and Metal are required in equal capacity to create a truly functional creature?
As for Animari summoning, I would say that it depends entirely on what school the creature would belong to. For example, the Lord of the Tempests is obviously spawned of Water, and the Walking Nuun is conjured by Fire. If something is blurred between the boundaries, perhaps it requires Animari philosophers of multiple disciplines.