B737-500 DIVERTS TO ALTERNATE WHEN FLAPS FAIL TO EXTEND BEYOND 10 DEGS AT DEST.

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ON RWY 27 LOC APCH TO ZZZ1; WHEN WE SELECTED FLAPS 15 DEGS; THE FLAPS STOPPED AT 10 DEGS. WE INFORMED THE TWR OF OUR FLAP ISSUE AND RECEIVED RADAR VECTORS FOR ANOTHER APCH TO RWY 27. WE COMPLETED THE PROCS IN THE QRH. WE WERE STILL UNABLE TO EXTEND THE FLAPS PAST 10 DEGS. QRH PROCS EXTENDING THE FLAPS ELECTRICALLY WITH THE STANDBY SYS DID NOT WORK. AT THIS POINT; WE WERE AT OUR MINIMUM FUEL TO GO TO ZZZ2 (WHICH WAS OUR PUBLISHED WX ALTERNATE). WE DECIDED DUE TO WX; PERFORMANCE CONSIDERATIONS; AND APCH FACILITIES AT ZZZ1 THAT A FLAPS 10 DEG APCH WOULD BE A SAFER OPTION AT ZZZ2. ZZZ2 HAS A LONGER RWY; BETTER WX AND BETTER APCH FACILITIES. WE RAISED THE FLAPS BACK UP AND DIVERTED TO ZZZ2. WE LANDED UNEVENTFULLY AT ZZZ2 WITH FLAPS 10 DEGS. SUPPLEMENTAL INFO FROM ACN 696658: THEY RETRACTED NORMALLY AND WE FLEW TO ZZZ2. ABOUT 40 MI FROM ZZZ2; THE APCH CTLR WANTED TO VECTOR US AND HAVE US SLOW TO 200 KTS. I ADVISED THEM THAT WOULD NOT WORK FOR US AND DECLARED WE WERE MINIMUM FUEL. THEY CLRED US DIRECT AND WE LANDED FLAPS 10 UNEVENTFULLY.