RSX Sludge Help

My RSX engine light was on and would not pass inspection. The car ran just fine. I took to the dealer who would diagnose for $125. I agreed. He sited sludge and said $950 to clean. I agreed. Went o pick up car dealer said Uh Oh car does not stay running. Said some of "sludge went into other parts of engine and car dies when idling. WHAT ? ? ? Dealer wants additional $5000 for new engine.
I am not mechanically inclined. Am I being taken advantage of ? But it sounds like the Dealership caused the problem by not cleaning properly. Am I wrong ? What should I do ?


Please help ? Anyone ?