Revert Season 4 Evelynn Nerfs
The new jungle and jungle itemization are serious nerfs to Evelynn already.
Why not just revert the damage nerfs you gave her at the end of Season 4? This would at least make her playable while you find a way to make her more viable.
Speaking of ways to make her playable ...
Proposal: (keep Q and E the same while moving around some things on the W and R)
Agony's Embrace
Active: Evelynn impales all enemy units in target 250-radius area, dealing magic damage equal to a percentage of their maximum health and slowing their movement speed for 2 seconds.
Magic Damage: 10 / 15 / 20 + (1% per 100 AP ) + (1% per 100 AD)
Dark Frenzy Passive: Evelynn's movement speed is increased by 10, 15 , 20, 25, 30 Active: Evelynn lashes out around her slowing all enemies in a 250-radius area and stealing their movement speed for 3 seconds. Evelynn removes all slows affecting her, and ignores unit collision while this is active. Champion kills and assists refresh Dark Frenzy's cooldown. Magic Damage: Slow and Steal %: 20, 30, 35, 40, 50 Shield Strength per champion hit: 50 / 125 / 200
(Obviously these numbers are just estimates. So please commenters, don't get caught up in them when assessing this.)
Basically -- her Ult becomes an execution (giving her some assassin potential) and her W gives her some team utility while providing a mechanism to close on her intended target and a chance to escape if she is successful in executing them. (with a mini shield and speed steal.)
Alright -- so now you're got an action plan.
Step 1: Revert Season 4 nerfs so we can play Eve now. Step 2: Make the changes requested above (and add the S4 nerfs back in.) Step 3: Profit.