Would a team of five assassins be good?
e.g Zed, Akali, Katarina, Talon, Shen
Shen is because he is a support, tank and can increase the burst on a target with Vorpal Blade.
Katarina is AP, so Armor wouldn't be as effective. Would this be a good team comp? You can each pick someone and burst them down almost immediately.
Short answer: No
Long answer: A lot more goes into an assassination than just damage. You need the CC to ensure your assassin can do their job, the Shields/Peel to ensure he doesn't immediately die, and most importantly, you need to have a team that can take advantage of the 4v5.
Every one of the assassins you list is more than capable of insta-gibbing a squishy with proper support, and late game, you only need one kill to end the whole thing. So, what are those other assassins doing for you? There's no real reason to have them. You'd benefit much more from having a tank to let you turret dive, an ADC to shove down towers, and a mage to push waves and defend yourself from sieges.
The team you list is also kinda awkward because no two of them are capable of laning against an ADC/Support duo, and none of them are particularly good junglers. So, you're handicapping yourself unnecessarily in that regard.
Currently, if you want a team that's really good at picking one guy and 100-0ing him, something along the lines of Gragas top, Elise jungle, Xerath mid, Tristana ADC and Thresh support is gonna be really, really good at doing that - but also really good at sieging turrets, pushing waves, teamfighting, taking down neutral objectives and laning. So even though on paper, it's worse at instagibbing people than the team you suggest, it's still good enough at that while being much more versatile.
Make sense?
no
Their is no reason why they couldnt be. As long a the people are skilled and you have a strategy you could make it work. :p
it would probably work against certain team compositions, the problem is you would have a lot of problem dealing with tanks, or pretty much anyone you can't one shot. Generally, I think 5 assassin comps would be a bit redundant, but there are more traditional looking comps that have 4-5 assassins. Not that this is a good comp, but you can have say, Zed top, Rengar jungle, Ahri mid, Tristana ADC, and LeBlanc support (it's really rare but it has happened in professional play).
