This team is designed to win games fast and efficiently.
--Laning, not exactly our strong point and that's saying a lot--
Doesn't really matter which solo takes mid as they both have their advantages. You could even put your duo lane in mid with your two solos on the side lanes if desired. Sivir is probably the weakest lane as her only defense is Spell Shield, which is rather sub par. If need be, Soraka can come help Sivir and leave Chogath on the defense.
Assuming all goes well, Shaco will have come out for 2-4 ganks and the other lanes may have pulled off a kill or two. There should most likely be one of the enemy towers very low or destroyed by the time you reach mid game (the preferred tower to get down early is mid).
---Mid game, now the fun begins--
Now that the pain is over, you should be able to win the game in the next 5-10 minutes. How this works - Shaco pushes one lane solo, preferably top or bottom; while the rest of your lane pushes on the other side of the map. You are exposing yourself to lose either a 1v5 or a 4v5, but this is ok as the other lane will get utterly decimated in the time it takes to finish the fight.
Should the other team decide to instead push your third lane (mid), Shaco can switch lanes and take out the creeps behind their push while Sivir ports back to defend. Effectively stopping them at the very least, outside your base.
If the enemy team continues to keep you pushed, maybe you lost early game or something, the 4 man can defend at the base while Shaco pushes an odd lane, their team will have to break off their push to defend their own base. If they don't stop Shaco's push, Sivir can port in and the two of them can destroy a whole base in a matter of seconds.
What late game? you guys won 10 minutes ago.