Abdominal aortic aneurysm: The patient's age, symptoms of severe abdominal and back pain, and the fact that a CT scan of the abdomen was obtained suggest that an abdominal aortic aneurysm (AAA) is a highly probable diagnosis. AAAs are more common in older adults and can cause severe pain if they rupture.

Pancreatitis: This condition can cause severe abdominal pain that radiates to the back. While it's less likely than an AAA given the context, it remains a plausible diagnosis, especially if the patient has a history of gallstones or alcohol abuse.
Peptic ulcer: A perforated peptic ulcer can cause severe abdominal pain and could potentially radiate to the back. However, the back pain component is less typical for peptic ulcers compared to AAAs.
Perforated diverticula: Diverticulitis with perforation can lead to severe abdominal pain and potentially back pain if the perforation leads to an abscess or peritonitis that involves the retroperitoneal space.

Ureterolithiasis: While kidney stones (ureterolithiasis) can cause severe pain, the pain typically is more flank-like and radiates to the groin. However, in older adults, the presentation can be atypical, and missing a stone could lead to severe consequences like sepsis if an obstructed kidney becomes infected.
Ruptured ovarian cyst: In postmenopausal women, a ruptured ovarian cyst can cause acute abdominal pain. Although less common, it's a diagnosis that should not be missed due to potential for hemorrhage.

Retroperitoneal hemorrhage from other sources: This could include bleeding from other abdominal or retroperitoneal structures not related to an AAA, such as a hemorrhagic transformation of a lymphoma or metastasis.
Inflammatory or infectious processes: Conditions like pyelonephritis, psoas abscess, or spinal infections could present with back and abdominal pain but are less likely given the acute presentation and the decision to obtain a CT scan of the abdomen.