A B737-300 ON FINAL APCH AT 3000 FT TRAILING EDGE FLAPS FAILED TO EXTEND FROM 2 UNITS TO 5 UNITS. EXECUTED GAR.

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CLRED FOR VISUAL APCH BY SOCAL FOR RWY 16L AT SMF; AND HANDED OVER TO TWR AT 3000 FT MSL ON RIGHT DOWN WIND. PF-CAPT CALLED FOR FLAPS 5-SELECTED 5 DEG POSITION AND NOTED THAT WE ONLY HAD SYMMETRICAL 2 DEG OF TE FLAPS-DUE TO PREVIOUS WRITE-UP AND MX CORRECTIVE ACTION; WE CYCLED FLAP LEVER FULL UP THEN BACK TO 5 DEG POSITION. WITH SAME 2 DEG TE RESULTING. WHILE DOING THIS WE HAD ASKED FOR AND RECEIVED A DOWNWIND EXTENSION; PLUS HANDOFF BACK TO SOCAL APCH. RAN QRH AND THEN UPDATED FLT SYS LANDING DATA FOR REDUCED FLAPS (1-15 DEG); INFO FROM ATIS AND LANDING WT 111.0-NOTED LANDING DISTANCE WAS NOT A FACTOR-ONLY BRACKET WAS FOR MIN BRAKING. TURNED BACK INBOUND FOR EXTENDED ILS FINAL FOR RWY 16L-APCH AND LANDING TOTALLY UNEVENTFUL. WE WERE TOTALLY UNAWARE OF DAMAGE DONE BY FLAP UNTIL POST FLT INSPECTION. ABSOLUTELY NO COCKPIT INDICATION OF ANY PROBLEM EXCEPT FOR REDUCED TE FLAPS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE CAUSE OF THE TRAILING EDGE FLAP FAILURE WAS CAUSED BY THE #3 FLAP TRANSMISSION. THE RPTR SAID MAINT ADVISED THE CREW THIS WAS A VERY RARE FAILURE. THE RPTR SAID WHEN THE FLAP TORQUE TUBES ROTATED ALL FLAP TRANSMISSIONS TO EXTEND THE FLAPS BUT THE #3 FLAP DID NOT MOVE CAUSING AN ASYMMETRICAL SHUTOFF.