The Sony FS5 is a bit of a peculiar camera.
While the specs seem great on paper, there are some major obstacles to actually using it on a production while trying to record 4K. With the new 1.1 firmware, Sony at least partially addresses these issues, as it's now possible to record 4K internally while sending out a signal from the HDMI or the HD-SDI. Unfortunately, you've got to pick which image you'd prefer to see, as when you're recording 4K internally, only one of the following outputs is enabled: SDI, HDMI, or Viewfinder/LCD.
You can download the update on the Sony site, and here are some more details on the output situation — it's clarified a bit better in the notes part (thanks to News Shooter for their terrific coverage of this camera and firmware update):
According to those in the know, this camera is hardware limited from being able to send a signal to all outputs simultaneously. We've come to expect all cameras just to be able to do this no questions asked, but obviously some corners were cut in order to make the 4K hardware cheaply enough and still offer all of these other features. If you're using this camera in a film set situation, it's likely that you'll need an additional external monitor to hang off the camera if you want to give your operator an image, and your AC an image on the side of the camera for pulling focus (unless you both don't mind fighting over a monitor). If you are recording to one of the fantastic external recorders out there, this isn't really an issue, as they are pretty much all capable of giving an HDMI or SDI signal for an additional monitor.
Hopefully it's something Sony can address in the future, but if you're an owner, or might be an owner, I wouldn't expect this to change anytime soon if it's even possible to send images to all outputs at the same time.