Final answer:
The client with pneumonia exhibiting bilateral crackles and diminished breath sounds should be assessed first due to the potential immediate threat to their airway and respiratory status, making it the highest priority.
Step-by-step explanation:
The nurse should assess the client with pneumonia exhibiting bilateral crackles and diminished breath sounds first. This patient's presentation suggests a potential acute respiratory compromise that can rapidly escalate, requiring immediate intervention to prevent further deterioration. Thus, the client with pneumonia is the highest priority due to the immediate threat to their airway and respiratory status. While the client requesting sublingual nitroglycerin for chest pain following a myocardial infarction (MI) also requires timely attention, the nature of the symptoms in the client with pneumonia indicates a more critical respiratory status. Pain management for the postoperative client and addressing severe itching for the client with atopic dermatitis, while important, is not as urgent as the respiratory issues presented.