2007 Mustang GT, Automatic transmission. Engine equipped with Variable Valve/Cam timing.(lash adjuster on engine valves) Every once in a while during the beginning of acceleration, I hear a click, usually 3 to 5 times in a row and then all is quiet. Doesn't do this all the time, just once in a while. Any ideas?

Try using full-synthetic engine oil and a premium filter (e.g. Mobil 1 EP or Purolator PureOne) and see if the noise goes away.

I have, Royal Purple 5w20 full synthentic since I bought the car. Used either fram, motorcraft or royal purples filter as well.

Engine knock often manifests itself in the valves, especially in hot weather. Experiment with a different brand of oil (e.g. Amsoil, Mobil 1, or Pennzoil Platinum) and/or possibly going to SAE 5W-30. Also, ensure the correct octane gas is used. Finally, I would only use Motorcraft spark plugs--the exact ones that came in the car, or the next colder plug. Change them every 40,000 miles.