How to calculate C for an AM demodulator?
\$\omega\$ is the angular frequency.
\$ \omega = 2\pi f \$
This makes your equation:
\$ C = \frac {1}{2\pi f R_Lm}\$
For your example:
\$ C = \frac {1}{2\pi (5000) (5000) (0.5)} = 0.01273239µF \approx 0.013µF\$
\$f\$ is the frequency of the modulation signal (5kHz,) not the carrier (15MHz.)