A 42-year-old woman from rural Maharashtra presents with a 3-month history of persistent cough and low-grade fever. Chest X-ray shows an upper lobe infiltrate. A tuberculin skin test (TST) is performed and reads 15 mm induration at 48 hours. In this population, the prevalence of active TB is 5%. The TST has a sensitivity of 85% and specificity of 90% for active TB. What is the positive predictive value (PPV) of this TST result, and what does it tell us about the likelihood of active TB in this patient?