We report on new 5-GHz Very Large Array (VLA) radio observations of the pulsar-powered supernova remnant G21.5-0.9. These observations have allowed us to make a high-quality radio image of this remnant with a resolution of similar to 0.7 arcsec. It has a filamentary structure similar to that seen in the Crab Nebula. Radio structure suggestive of the torus seen around the Crab pulsar is tentatively identified. We also compared the new image with one taken similar to 15 yr earlier at 1.5 GHz, both to find the expansion speed of the remnant and to make a spectral index image. Between 1991 and 2006, we find that the average expansion rate of the remnant is 0.11 +/- 0.02 per cent yr(-1), corresponding, for a distance of 5 kpc, to a speed of 910 +/- 160 km s(-1) with respect to the centre of the nebula. Assuming undecelerated expansion, this expansion speed implies that the age of G21.5-0.9 is 870(-150)(+200) yr, which makes PSR J1833-1034 one of the youngest, if not the youngest, known pulsars in the Galaxy.