A B737-500 FLT CREW EXPERIENCED AN ASYMMETRICAL TRAILING EDGE FLAP CONDITION ON APPROACH. THEY RAN THE QRH PROCEDURE AND LANDED.

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INSTRUCTED BY ATC TO SLOW TO 180 KTS; SELECTED FLAPS 5 DEGS. THE R TRAILING EDGE FLAP CONTINUED TO INDICATE 'UP;' THE GAUGE NEEDLE BARELY MOVING. THE L TRAILING EDGE FLAP NEEDLE MOVED MORE THAN THE R; BUT ALSO STOPPED AT LESS THAN FLAPS 1 DEG. I CALLED FOR THE FLAPS; TRAILING EDGE: SYMMETRICAL NON-NORMAL/NO FLAPS CHKLIST. WHILE USING THE ALTERNATE FLAPS SWITCH; THE TRAILING EDGE GAUGE NEEDLES INITIALLY MOVED PARALLEL; AND IN FACT BEGAN TO COME BACK TO MATCH. AS THE TRAILING EDGE FLAP POS PASSED THE FLAPS 2 DEG POS; THE NEEDLES BEGAN TO DIVERGE. AT THAT POINT I IMMEDIATELY RELEASED THE ALTERNATE FLAPS SWITCH AND CONTINUED WITH THE FLAPS; TRAILING EDGE: ASYMMETRICAL CHKLIST. THE LEADING EDGE FLAPS TRANSIT LIGHT REMAINED ON AS ADVERTISED FOR A MINOR TRAILING EDGE FLAP POS; BUT ALL INDICATIONS ON THE OVERHEAD PANEL FOR LEADING EDGE FLAPS WERE NORMAL. WE RAN OPC LNDG DATA AND IN COORD WITH THE OPS SUPVR AND ATC CHOSE TO CONTINUE THE PLAN TO LAND AT ZZZ1 AND SELECTED RWY XX AS THE BEST OPTION FOR LNDG UNDER CURRENT CONDITIONS. REFLECTING UPON THE EVENT; AND AFTER SPEAKING WITH THE CHIEF PLT'S OFFICE; THE CONCERN AND REASON FOR WRITING THIS RPT IS: ALTHOUGH A SMALL SPLIT IN THE TRAILING EDGE FLAP NEEDLES IS NOT UNCOMMON IN THE -300/-500 ACFT UNDER NORMAL OPS; IN HINDSIGHT; IT WOULD OBVIOUSLY HAVE BEEN MORE PRUDENT TO ASSUME THE WORST CASE AND PROCEED DIRECTLY TO THE FLAPS; TRAILING EDGE: ASYMMETRICAL CHKLIST. AGAIN; ANY SPLIT; NO MATTER HOW SMALL; IN TRAILING EDGE FLAP GAUGE NEEDLES SHOULD PROBABLY BE ASSUMED TO BE AN ASYMMETRICAL CONDITION IF THE TRAILING EDGE FLAPS ARE NOT RESPONSIVE TO LEVER POS. THE QRH IS PRETTY CLR ON ASYMMETRY. PROBABLY JUST SLOWING DOWN AND NOT ALLOWING THE HEAT OF THE MOMENT AND OTHER ISSUES TO CLOUD THAT FACT AND MAKE OTHER ASSUMPTIONS; IS THE BEST SOLUTION.