In an effort to reduce the cost of sensing systems and make them more compact and flexible, Brillouin scattering has been demonstrated as a useful tool, especially for distributed temperature and strain sensing (DTSS), with a resolution of a few centimeters over several tens of kilometers of fiber. However, sensing is limited by the Brillouin frequency shift's sensitivity to these parameters, which are of the order of ~1.3 MHz/°C and of ~0.05 MHz/με for standard fiber. In this Letter, we demonstrate a new and simple technique for enhancing the sensitivity of sensing by using higher-orders Stokes shifts with stimulated Brillouin scattering (SBS). By this method, we multiply the sensitivity of the sensor by the number of the Stokes order used, enhanced by six-fold, therefore reaching a sensitivity of ~7 MHz/°C, and potentially ~0.30 MHz/με. To do this, we place the test fiber within a cavity to produce a frequency comb. Based on a reference multiorder SBS source for heterodyning, this system should provide a new distributed sensing technology with significantly better resolution at a potentially lower cost than currently available DTSS systems.