Final answer:
The most likely diagnosis for the 62-year-old male with a productive cough, shortness of breath, and signs of respiratory distress is pneumonia, based on his symptoms and clinical findings.
Step-by-step explanation:
The symptoms presented by the 62-year-old male patient are suggestive of pneumonia. The productive cough, worsening shortness of breath, mild respiratory distress, and coarse crackles in the left lung base on auscultation, coupled with an oxygen saturation of 91% on air and elevated temperature, point towards an infection of the lungs. Considering his background of asthma, which could predispose him to pulmonary infections, and the absence of smoking history which reduces the likelihood of chronic obstructive pulmonary disease (COPD), pneumonia appears to be the most likely diagnosis. Additional diagnostic tests, such as a chest radiograph, sputum culture, and possible blood tests, would further help to confirm pneumonia and the causative organism.