We present new continuum VLA observations of the nearby Sy 1.5 galaxy NGC 5033, made at 4.9 and 8.4 GHz on 8 April 2003. Combined with VLA archival observations at 1.4 and 4.9 GHz made on 7 August 1993, 29 August 1999, and 31 October 1999, we sample the galaxy radio emission at scales ranging from the nuclear regions (<~ 100 pc) to the outer regions of the disk (~ 40 kpc). The high-resolution VLA images show a core-jet structure for the Sy 1.5 nucleus. While the core has a moderately steep non-thermal radio spectrum (S_ u ~ u^alpha; alpha_{1.5}^{4.9} approx -0.4), the inner kpc region shows a steeper spectrum (alpha_{1.5}^{8.4} approx -0.9). This latter spectrum is typical of galaxies where energy losses are high, indicating that the escape rate of cosmic ray electrons in NGC 5033 is low. The nucleus contributes little to the total 1.4 GHz radio power of NGC 5033 and, based on the radio to far-infrared (FIR) relation, it appears that the radio and far-infrared emission from NGC 5033 are dominated by a starburst that during the last 10 Myr produced stars at a rate of ~2.8 M_sun/yr, yielding a supernova (type Ib/c and II) rate of 0.045 #/yr. This supernova rate corresponds to about 1 SN event every 22 yr. Finally, from our deep 8.4 GHz VLA-D image, we suggest the existence of a radio spur in NGC 5033, which could have been due to a hot superbubble formed as a consequence of sequential supernova explosions occurring during the lifetime of a giant molecular cloud.