Champions

[Kaden]

Cho'gath can be built AP, and that's what I was doing.

You realize that wasn't, at all, his point, right? >.>

I think the best way to work on 5s comps is to start with who plays what before even clicking the "start game" button. It gets things started, but on a very rudimentary "what does this even mean" level. In the situation Ashe described, Trist was absolutely the right pick. It should have been Tryg's, though. Whoever grabbed the second AD should have either traded it down and picked something else that hadn't already been spoken for. Look at the diversity that you still have by just calling a lane/archetype:

Solo top/bruiser: Riven (late game ad), Tryn (hyper carry ad), Rumble (AP bruiser), Morde (AP bruiser/pusher), Akali (AP assassin), Talon (AD assassin), Udyr (tank/utility beast-man)

Mid: Ryze (tanky, low-AP magic dmg carry), Veigar (anti-caster AP carry), Cass (AP carry, pusher, AoE), Kat (tonsofdamage AP carry, AoE), Panth (AD caster), Orianna (AP carry, utility, AoE), Karthus (zombie, global ult)

Duo bot AD: Trist (positional control, hyper carry), Ashe (super utility, global stun), Corki (super damage, no CC, AoE), Vayne (FUCKING % TRUE DAMAGE, single-target beast), Sivir (pusher, buffs

Duo bot Support: Janna, (CC, disengagement, goddess slut of assists), Leona (tanky, CC galore), Sona (super sustain, disengagement, buffs), Soraka (burst heal, AoE, silence, sustain), Taric (CC, AoE, buff, roaming, buffs), Ali (CC, sustain, roaming, tanky), Gangplank (he eats fruit)

Jungler: Shaco (fuck this guy. seriously), Trundle (super debuffs, AD bruiser), Nocturne (long-range ult, AD carry), Nunu (counter jungle, AoE, CC, buff)

Those are only a few examples. There's SO much that can be done within any given archetype. Picking one is just a great place to start working on comps that have a lot of synergy.