My crew and I were flying our aircraft from Cairo Egypt to Dhahran Saudi Arabia. When our location was approximately due south of Tabuk (unk distance), we spotted a star like object in the distance off of our right wing(200 heading) and at about 30-50 miles. Within seconds a very bright beam had projected down onto the cloud deck below like a searchlight. The searchlight itself did not appear to be actively moving.Our aircraft was at approximately FL 210-230, heading approximately 110 degrees. The object The object was at a similar altitude, appeared stationary and the cloud deck below was around 10-12K MSL.At first we thought it was another aircraft but there was little chatter on the ATC frequencies that would indicate traffic in our area. A helicopter was ruled out due to altitude. Their were no anti-collision lights nor navigational lights from the object that could be seen.It is possible a RSAF C-130 based at Jeddah was conducting night operations and the retracted landing lights could have been turned on causing the "searchlight" appearance. The lack of other lighting makes this unlikely.The only initial feeling aboard the aircraft was of puzzlement This faded fairly quickly as explanations were running out and it seemed as if the other crew members would rather forget about the sighting.The object was in our view for about 3-5 minutes before we lost sight of it as it passed behind our aircraft.I do not have charts and flight logs available to give more accurate information.There was no significant weather in the area.