Perfect team would be a full team of people that know all the roles and excel in each role. If you have an awesome comp and counter all of the opposite team you still might lose because of derpy teamates.

Solo top/jungle/mid/bot/support: Lee Sin.

1v5, good luck and godspeed other team.

Also, I call this the blender:

Garen
Garen
Garen
Garen
Garen

5 Spin to Win. u jelly?

Solo top: Vladimir or Gangplank, depending on the enemy team
Duo mid: Morgana as a support + Ahri / Malhazar / Cassio
Solo bot: Magewick or Nidalee, basically anyone who is hard to chase out of the lane and can 1vs2
Jungle: Nocturne

That would be awesome if we could have multiple of the same champ on the same team. 5 Karthus on the same team omg so epic. All 5 ults at the same time late game = 5500 damage on each champion

top riven
mid malzahar
jungle lee sin
adc caitlyn
support janna

#thank me later

My dream team would be
Morgana and Ad Kayle bot sustaining themselves
Annie mid with
Amumu in the Jungle ganking for her
Ad Poppy Solo top

If I was allowed to break the meta I would do this
Garen and Lux bot
Caitlyn Solo top
Akali mid with
Pantheon in the jungle ganking for everyone

On the other hand this always looked fun as well
Swain and Annie bot
Caitlyn solo top
Talon mid with
Amumu in the jungle again

Top lane: a lot of choices. Just the ones that become monsters when farmed. Riven or Nasus come to mind but it could easily be someone else.

Jungler: Skarner, Lee Sin, Shyvana. I want tanky bruisers that are going to have no reservations about going balls deep into the enemy team. Skarner is exceptional because of his initiation and constant disruption due to aoe slow. That and he's incredibly tanky vs AD and his damage output is massive.
Shyvana has no cc but makes up for it by being a ****ing dragon, being in their face and really screwing up their positioning just by being in their face. Lee has great ganks and a lot of counter-jungling opportunities. Aoe slow + attack speed debuff is great in teamfights and has some of the same qualities as Skarner but just not constant.

Ap mid: Cass, Kennen, Karthus High consistent damage and very strong ults, combined with great crowd control. What's not to love?

Support: Janna If your ad carry doesn't play full ****** then you don't need sustain. Her constant disruption allows your bruisers to stick to their targets and allows you to peel entire teams off.

Bot ad: any of the top ad carries. I would pick sivir but that's just me.

Janna, Skarner, and Kennen would make any initiation on your team backfire in your enemy's faces. They just let your solo top and ad bot do their jobs and tear into the enemy without much retaliation. Throw into that mix some disruption from Riven or a Nasus... or Shen, or Renek, etc.. all this while your ad carry is safe behind bruisers and multiple peel options with +50dmg from Janna's shield.

ya now I wanna try this.

Soraka _ Best Champ
Taric
Karma
Volibear
Caitlyn

ap mid ---> Ahri
top ---> Gp
jungle tank ---> Naut
bot ---> Karma + Tf

dont think anyone can find something better ^^
very hard to counter this team if well played

My dream team:

Everyone except the AD carry uses wards, always buying 1-2 each b. And the AD carry might even buy 1 or 2 as needed.

All the players watch the map more than the main game screen. (And nobody plays with locked cameras.)

Every player is at least comfortable in every role, and is willing to switch it up as necessary. "Oh no, they countered with Olaf top. I know you were gonna do Kennen mid, but go top, I'll handle mid."

Nobody rages. Frustration is okay, but there's more "gj" and "ty" in the chat than "omfg gg!"

Everyone on the team has at least 3-5 champs for each role, and is familiar with all of them to some extent. Ideally, everyone would have 60-70+ champs to facilitate trading during team select.

Actual champs are inconsequential before the match starts, and are determined by picks/counter-picks during team select.

Anyway, that's my ideal team comp for now.