Accessory Quest Rank 5 will likely be introduced Christmas 2018. These use the same materials as Rank 3 to spawn, always drop an SSR accessory, and can drop an upgraded "Ancient" SSR accessory with higher stats and stronger effects.
Rank 5 is extremely difficult. The final boss has a 5-orb overdrive meter, and uses a lethal AoE overdrive (normal or raging). This must be near-total mitigated using damage cuts and elemental resistance, or the boss must be stunned before it can use it. I've outlined both strategies in my
Endurance and
Rapid Burst builds.
Furthermore, AQ5 bosses have high affliction resistance, combo attack frequently, and hit hard (~3k/hit without debuffs). Landing debuffs on a boss of the same element is likely to be extremely difficult. Elemental advantage can ameliorate the affliction resistance to some extent, but then you have to commit to raising every single grid and spending a lot of money on SSR Kamihime Gatcha.
You can get a taste of what fighting one of these bosses could be like with a typical team without elemental advantage from this video. (Note that he would've taken 0 damage from the Overdrive with Joan's HP Relic weapon, and a similar team with Joan's weapon could mitigate damage equivalently with an SR Dragoon instead of Gaia, or much better with an SSR Kaiser). I picked this video in particular because the user doesn't trivialize the fight with 2x +100% eidolons or other cheese that won't be available to most players, nor is he relying on DEF debuffs that might miss and cause the fight to play out entirely differently.
video
Why bring this up now? Because we'll need to use Miracle tickets strategically to be able to defeat these. I'm personally trying to determine which would be more effective: a combination of one excellent Wind team and an ok Water team, or a single excellent Light team. The Light team has the advantage of built-in affliction resistance down with Light Tsukuyomi. A comparable Wind Endurance build would need to run Black Propaganda (and therefore wouldn't have access to Vicissitudes of Fortune), while a Rapid Burst build could run VoF, but would likely be extremely dependent on DEF down landing. The Rapid Burst build would be unlikely to survive 1 Overdrive with -50% ATK down and 70% damage resistance (Gaia + SSR Kaiser).