What was found
EN ROUTE FROM PHX TO IAH WHILE AT CRUISE ALTITUDE FL350/.75 MACH, THE LEADING EDGE FLAP TRANSIT LIGHT ILLUMINATED AND NR 5 SLAT TRANSIT (AMBER) LIGHT ON OVERHEAD PANEL. INITIALLY SEEMED TO BE FALSE INDICATION, BUT WHILE DOING QRH CHECKLIST THE YOKE BEGAN TURNING TO THE RIGHT TO ABOUT 3 UNITS. DISCONNECTED AUTOPILOT AND SAME RESULTS. DECLARED AN EMERGENCY AND DESCENDED/SLOWED DOWN AND DIVERTED TO ELP. AT SOME POINT APPROACHING ELP, THE AMBER CAUTION LIGHT AND OVERHEAD LIGHT WENT OUT. CONFIGURED THE AIRCRAFT FOR CONTROLLABILITY CHECK AND WITH FLAPS EXTENDED TO 15, CONTROL FELT NORMAL, BUT EXPERIENCED TWO SUDDEN REQUIREMENTS FOR A LOT OF RIGHT AILERON BUT THEN NO REOCCURRENCE. LANDING WAS ACCOMPLISHED UNEVENTFULLY. MAINTENANCE PERFORMED VISUAL INSPECTION OF ALL SLATS, FLAPS, SPOILERS AND AILERONS. OPERATED FLAPS, SLATS, AILERONS AND SPOILERS NUMEROUS TIMES. NO VISUAL OR OPERATIONAL DEFECTS NOTED. NO UNUSUAL INDICATIONS NOTED. AIRCRAFT WAS MAINTENANCE FERRIED TO PHX. ON FOLLOW UP MAINTENANCE, MAINTENANCE FOUND THE NR 4 SLAT ACTUATOR MOVING SLOWLY. REPLACED NR 4 SLAT ACTUATOR. OPS AND LEAK CHECK GOOD. AS PRECAUTIONARY, MAINTENANCE ALSO REPLACED THE NR 5 SLAT ACTUATOR. OPS AND LEAK CHECK GOOD.