Notice who had the most kills on your team? The apc nuker/assassin Ahri? Yeah.
The team is overspecialized. There is no frontline to protect from burst damage, no bruisers to take out assassins, no supports to apply cc and protect key carries, no assassins/nukers to even touch the backline (Ezreal may count, however).
It's just not balanced. ADCs are the most item-dependent class, hell one of their main items for their core costs 1550 gold! At least mages have more options than that!
Seriously, I could probably penta them as Vi just by building
. Okay, maybe not, but any team comp with the right balance and tools could easily wreck them (as you guys apparently did).
However, you could do off-builds. Bruiser Vayne, support Ashe, blue Ezreal, and so on. It can work, maybe.