Final answer:
The most likely etiology of the pleural effusions is Congestive Heart Failure. Pulmonary edema is a common symptom of heart failure that can lead to excess fluid in the air sacs of the lungs.
Step-by-step explanation:
The most likely etiology of the pleural effusions in this case is Congestive Heart Failure. Pulmonary edema, which is excess fluid in the air sacs of the lungs, is a common symptom of heart failure. The patient's symptoms, medical history, and physical examination findings are consistent with heart failure. Additionally, the pleural fluid characteristics, such as turbidity, elevated white blood cells count, and the protein and LDH ratios, are indicative of a transudative pleural effusion caused by heart failure.