Ulnar nerve compression or injury: This is the most likely diagnosis due to the specific involvement of the fourth and fifth fingers, which are primarily innervated by the ulnar nerve. Compression or injury to this nerve can occur at various points, including the elbow or wrist, leading to weakness and potentially other symptoms like numbness or tingling in these fingers.

Cervical radiculopathy (C8 radiculopathy): This condition involves nerve root compression in the cervical spine, specifically affecting the C8 nerve root, which supplies the fourth and fifth fingers. Symptoms can include weakness, pain, and sensory changes in the affected fingers.
Brachial plexopathy: Although less specific, brachial plexus injuries can affect the lower trunk, which includes fibers from the C8 and T1 nerve roots, potentially causing weakness in the fourth and fifth fingers among other symptoms.
Stroke or cerebral vasculature issues: While less common for such localized symptoms, a small stroke or other cerebral vascular issues affecting the motor areas of the brain corresponding to the hand could potentially cause focal weakness.

Acute coronary syndrome or cardiac issues leading to embolic stroke: Although the presentation is atypical for a stroke, any new onset of focal neurological deficits warrants consideration of a stroke, especially in a 77-year-old. Prompt diagnosis and treatment of a stroke can significantly improve outcomes.
Tumors (e.g., Pancoast tumor): A tumor in the apex of the lung (Pancoast tumor) can compress the brachial plexus, leading to weakness and other symptoms in the arm and hand. Given the potential for serious underlying conditions, these diagnoses should not be missed.

Mononeuritis multiplex: This is a form of damage to multiple peripheral nerves that can cause weakness and sensory loss in the areas supplied by the affected nerves. It could potentially present with weakness in the fourth and fifth fingers if the ulnar nerve is involved, among other nerves.
Neuropathy due to systemic disease (e.g., diabetes, amyloidosis): Certain systemic diseases can cause peripheral neuropathy, which might manifest as focal weakness, including in the distribution of the ulnar nerve. However, these conditions typically have a more widespread or bilateral presentation.
Inflammatory or autoimmune conditions (e.g., multifocal motor neuropathy): These conditions can cause focal or multifocal weakness due to immune-mediated damage to the nerves. They are less common and might present with a variety of neurological symptoms, including weakness in specific muscle groups.