Last game I was against a team which had massive poke and some sustain. To make things worse they also got baron. With that they could just stay behind their minions and launch skill after skill wiping out big chunks of health every time they hit one of us. In the meantime their minions were covered by their endless skill spam and could take down a turret slowly.
Our team was: Gnar, Rek'sai, Swain, Graves and Braum.
Theirs was: Jayce, Nidalee, Xerath, Caitlyn and Sona. Nidalee was a pretty tanky cat though...
So how to deal with a team (or minions) that is sieging and has a lot of nasty poke?