Final answer:
The most likely cause of the man's symptoms, given the severe epigastric pain, vomiting, and mediastinal crackles, is a transmural esophageal rupture.
Step-by-step explanation:
The symptoms described by the 56-year-old man, including severe epigastric pain radiating to the back, exacerbated by swallowing and cough, along with a history of vomiting and prior hospitalizations for acute pancreatitis, leans towards a diagnosis of transmural esophageal rupture (option e). This condition is also known as Boerhaave syndrome and is consistent with the mediastinal crackles heard during physical examination, which may be indicative of air escaping from the esophagus into the mediastinum (mediastinal emphysema). While the other options are differential diagnoses for chest or abdominal pain, the specific symptoms and clinical signs provided are most characteristic of an esophageal rupture.