Aperture sometimes quits when starting up after you install Mac OS X 10.5 Leopard.
This can happen if you use Aperture 1.5.4 or earlier. Update to Aperture 1.5.6 or later to resolve this issue. You can get the Aperture 1.5.6 update here. Additional information about the Aperture 1.5.6 update can be found here.