Would I be able to use a Canon XL1s lens on a Canon EF-mount camera, such as the 5D, without an adapter? I'm looking to purchase one for my camera but I'm not sure if it will work.
Without an adapter: Absolutely not.
With an adapter (that you would likely have to make yourself since no one sells such an adapter): Possibly, if you are willing to accept several limitations that would probably make the entire proposition not worth it to most people.
The image circle projected by the XL1 lens is only about 9mm wide. The diagonal of the 5D or any other full frame camera is about 43mm. At best you would have a small circular image in the middle of the sensor covering about 7.5% of the total sensor area. The registration distance of the XL1 lens is 29mm, the registration distance of the EF mount is 44mm. That means that the XL1 lens would be too far from the sensor to focus at anything except very close distances.
You might have a little better luck with an APS-C EOS-M camera that uses the EF-M mount. The Canon EOS-M system that uses the EF-M mount has a registration distance of 18mm, which would leave 11mm thickness to make an XL1 to EF-M adapter and still allow you to focus all the way to infinity. Since the EOS-M can be easily adapted to use EF lenses, one would assume it would also be fairly easy for an EOS-M camera to control the electronic aperture of the XL1 lens. Of course the APS-C sized sensor of an EOS-M would still be significantly larger than the image circle projected by the XL1 lens. The diagonal of a Canon APS-C sensor is about 27mm, so the image circle projected by the XL1 lens would cover more of the frame - about one fifth of the sensor's total area.