I'm actually having a 4 player lan soon with friends.
We make a spreadsheet on google and give us all access to it to share ideas.
We each blitz out some games, in order to form a list of proposed games. And then everyone gets a vote on each game, as to whether they want to play it, might play it or would not play it.
The games we considered this time, as part of this mind splurge of ideas, were: AoE 2, Borderlands 2, Broforce, Day Z, Diablo 3, Dungeon Siege, Forced, Guns of Icarus, Minecraft, Monaco, Rise of Nations, Rust, Saints Row, Settlers 3, Space Engineers, Starcraft 2, Terraria/Starbound, TF2, Titan Quest, Trackmania and Vegas 2.
I think you might find it a bit more difficult with 5 people, but I think this method is quite a good one. Doesn't put the emphasis on one person to come up with all the ideas as well, more collaborative.
The idea is to say that no game is a bad game to suggest to the list (I even suggested one to our lan which I said 'no' to), but just to put down everything you think of and let the voting later take care of whether you want to play it or not.