Final answer:
Prophylaxis with trimethoprim/sulfamethoxazole in a 56-year-old HIV-positive man is warranted due to his CD4 cell count being below 200, indicating a high risk for opportunistic infections such as Pneumocystis jiroveci pneumonia.
Step-by-step explanation:
The detail of the 56-year-old man's history that warrants the prophylaxis with daily trimethoprim/sulfamethoxazole for Pneumocystis jiroveci pneumonia (PCP) prophylaxis is his CD4 cell count being below 200.
Patients with HIV are diagnosed with AIDS when their CD4 T-cell count drops below this threshold, which significantly compromises their immune system, leaving them highly susceptible to opportunistic infections like PCP.
PCP prophylaxis is typically recommended for HIV-positive individuals with a CD4 count <200 to prevent the onset of this potentially fatal pneumonia.