Engine makes a moaning sound when running....started suddenly this afternoon.

What is your question?

Never happened before. A/C is not on. Driving in "Drive" setting. No warning lights on. Performance of car unaffected. Do smell something burning under the hood. No smoke, though. 2005 Lexus ES330, about 53,000 miles on it. Timing belt was replaced this past winter. All fluids changed. Oil is changed regularly. No leaks of anything detected in driveway.

What makes this problem better or worse?

Nothing makes better or worse.

How long has your 2005 Lexus ES330 had this problem?

A half an hour.