Well you can certainly share Aperture _photo_ to Facebook. You can create Facebook albums. I don't know that you can share slideshows, per se, but the relevant photos and then people can click through them on Facebook.
You will need to export the slideshow to the Finder. That will make QuickTime movie of it. Then upload that to FB. I would note that many folks report problems with FB rejecting their slideshow because of copyright issues with the music.