Third- and fifth-harmonic generation by ultrashort laser pulses in the mid-infrared (mid-IR) reveals nonlinear-optical effects beyond the fifth-order nonlinearity and enables, because of an extraordinarily long coherence length, efficient multiplex frequency upconversion of ultrashort mid-IR pulses. We show that harmonic generation by mid-IR pulses provides an access to the key optical constants of gas media, allowing metrology of linear and nonlinear-optical susceptibilities in the mid-IR and offering a tool for the remote sensing of the atmosphere.