Note: 1 hp = 33,000 ft·lb/min = 396,000 lb·in/min
$T = \dfrac{P}{2 \pi f} = \dfrac{5000(396\,000)}{2\pi(189)}$
$T = 1\,667\,337.5 \, \text{lb}\cdot\text{in}$
$\tau_{max} = \dfrac{16T}{\pi d^3} = \dfrac{16(1\,667\,337.5)}{\pi (14^3)}$
$\tau_{max} = 3094.6 \, \text{psi}$ answer