If you did not buy Apeture from the AppStore, you can download an update to Aperture 3.4.5 from the Apple Support Downloads page:
Aperture 3.4.5
Backup your Aperture library before you run the update installer and open Aperture for the first time. The upgrade from AP 3.2 to 3.4.5 will upgrade your Aperture library to a new format and that will completely rebuild the library. It is safer to have a backup. Aperture needs to be installed in the "Applications" folder, not a subfolder of Applications, and be called simply "Aperture" without any add ons.
After that try again to update to Aperture 3.5 from the AppStore. If you did not buy from AppStore, this update will change your Aperture licence to an AppStore licence, so be sure to sign into the AppStore with exactly the AppleID that you want to use for updatig and buying software.
For some posters here the Aperture 3.5 update was not visible, unless the primary sytem language was set to "English U,S," and the region to "United States". If you are living in a different country, try to change the "Language & Region" settings in the System Preferences and restart the system, before tring to update.
That should also trigger updates for the iLife apps and iWork.