B747-400 Captain reported a STAB TRIM UNSCHEDULED EICAS message on climbout. The fight crew elected to conduct an air turn back and make a precautionary landing at departure airport.

Narrative

After takeoff while in the climb about 4;000 feet to level off at 5;000 feet which was our clearance altitude with auto pilot off we got a EICAS message stab trim unscheduled. There was no change felt in the flight controls and a check of the trim tab show no signs of moving or movement. I called for the QRH and asked the First Officer to engage the autopilot. We leveled off at 5;000 feet and proceeded with the QRH. ATC cleared us to climb to 15;000 feet at which time we notified ATC that we would like to remain at 5;000 feet while we work on an issue and complete a check list. After completing the QRH; autopilot center and right would not engage. We elected to return to our departure airport. We notified ATC and got radar vectors to the airport for an ILS approach and landing without incident. We went back to the ramp and after finally getting a parking spot; the item was entered in the airplane log book.This failure was cause by flight control computer failure; which may be a result of the airplane sitting in extreme cold weather for a few days.I'm not sure of what could have prevented this failure as the cold weather is unavoidable. Maybe not having the airplane sitting in extreme cold weather could have help.