OP: did you buy this guitar from someone? It may be that it has been deliberately set high for slide playing. If this is the case, with a Floyd Rose trem, the easiest way to do this is with neck shims that deliberately set the neck with a higher angle. Dr.Kev mentions neck shims. I do not like Floyd Rose trems due to the need for shims for finite saddle height adjustment; a really awful design.
Do not take your guitar to a tech yet; a complete waste of money; learn to fish! Watch the video banjoplayer linked to and set the neck relief first; based on the pics this will do nothing for action but this is one variable put to bed. Next, I would block the trem so that it is flat to the top of the guitar, tune to pitch, remove block and adjust the trem claw screws to re-flatten the trem.
Next, check the trem pivot or bridge posts; it's possible that they are screwed out, lifting the whole bridge. Try screwing them in and see if the bridge height drops; this is the most likely reason for your high action.
Then, if still too high, remove the bottom E from the Floyd Rose, undo the bridge lock screw and lift the saddle to look for shims. Remove the shim(s), put it back together and assess the impact on action. If the problem is solved, repeat with the other 5 strings; don't mix the saddles around; they are position-specific.
If the action is still too high then the neck angle is too high. At this point, I would remove the neck and go looking for shims. This may be the point at which you may be more comfortable taking you guitar to a luthier for adjusting the angle correctly.
Good luck