Final answer:
A Chest Computerized Tomogram is the most appropriate next test to perform to identify the cause of pleural effusion in the presented case of a 57-year-old man with dyspnea and absent breath sounds in the lower left lung zone.
Step-by-step explanation:
To find the cause of the effusion in a 57-year-old man with a history of hypertension and smoking who presents with progressive dyspnea on exertion, left lumbar colic, mild ankle swelling, and notably absent breath sounds in the left lower lung zone, the most appropriate test to perform next is a Chest Computerized Tomogram (option 2). This imaging test will allow for detailed visualization of the chest and lung anatomy, helping to identify the cause of the pleural effusion, such as a malignancy, empyema, or other pathology that might not be evident with sputum analysis or culture alone.
Since there is no history or symptoms strongly suggesting tuberculosis (i.e., no cough, orthopnea, paroxysmal nocturnal dyspnea, or sputum production indicating likely infection), sputum AFB (option 3) might not be initially warranted. A pleural biopsy (option 4) could also be considered but is generally performed after imaging if there is suspicion of malignancy or in cases where pleural fluid analysis and imaging have not provided a diagnosis. An abdominal sonogram (option 5) is more focused on abdominal pathology and would not be the primary investigation for lung pathology.