Final answer:
The symptoms presented by the patient with end-stage AIDS and a low CD4 count of 50/μL most likely suggest a diagnosis of Vacuolar myelopathy, a condition associated with severe immunosuppression and spinal cord damage.
Step-by-step explanation:
The most likely diagnosis for a 45-year-old man with end-stage AIDS and a CD4 count of 50/μL who presents with symptoms of rapidly progressive gait difficulty, spasticity, leg weakness, sphincter dysfunction, and loss of proprioception to both feet and legs is C. Vacuolar myelopathy. This condition is commonly associated with severe immunosuppression in AIDS patients and is characterized by damage to the spinal cord, particularly in the thoracic region, leading to symptoms evident in this patient. While other options like progressive multifocal leukoencephalopathy, distal sensory polyneuropathy, neurosyphilis, and HTLV-1 myelopathy could present with similar symptoms, vacuolar myelopathy is more consistent with the combination of gait difficulty, spasticity, and weakness along with bowel and bladder dysfunction and sensory loss seen here.