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Just push with turret(s) and use basic attack on minions and try getting the killing blows for gold. As for the champions, use the grenade on them if they come near your turrets (I think you turrets automatically attacks them) and then you have to move around to a certain spot to hit them with missiles (Try avoid minions to prevent missiles from hitting them instead of the champion you want to kill).
This is where you become useful. Your turrets are already level 5. You can easily push minions at this point and get easy kills if you time your grenade correctly. Then you have a choice to activate your ulti and launch some missiles. It's safer to launch missiles while your ulti is active (since it shoots 5 instead of 3).
Best part, you can have 2 turrets solo the jungle at the buff monsters (while that happens, you can run into a lane and push). At this point, you should be able to kill minions in one shot (either grenade or missiles). Then to get ahead of the lane a bit, you can also go around and place 2 turrets behind the enemy's turret so it can halt incoming minions (this allows your minions to continue attacking the enemy's turret without being interrupted).
I made this build myself =].