A B737-300 FLC TAXIES THE WRONG WAY DOWN RWY 5L UNDER LOW VISIBILITY CONDITIONS THAT CREATED A POTENTIAL CONFLICT FOR THE GND CTLR AT IND; IN.

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IND ORIGINATOR. WX VISIBILITY AT 1/16 FT. HELD AT GATE UNTIL XA45; 1 HR 15 MINS LATE. WX IMPROVING; PUSHED AND TAXIED TO HOLD SHORT AT TXWY A4 ON TXWY A. #5 IN LINE FOR DEP ON TXWY A. RVR FOR RWY 5R IMPROVED TO THE EXTENT GND CTL STARTED MOVING ACFT TO DEPART RWY 5R. GND WAS TAXIING ACFT DOWN TO RWY 5L TO THE END AND AROUND ON TXWY P AND TXWY C TO RWY 5R. AFTER A SHORT DISCUSSION; THE CAPT AND I DECIDED; DUE TO THE IMPROVING VISIBILITY AND THE NUMBER OF ACFT HEADED FOR RWY 5R; WE WOULD LIKE TO CONTINUE ON TXWY A AND DEPART RWY 5L. TO THE BEST OF OUR RECOLLECTION HERE WAS THE XMISSION SEQUENCE: WE SAID TO GND; 'GND FLT X; WHEN AVAILABLE; WE WOULD LIKE TO CONTINUE TAXI TO DEPART RWY 5L.' GND IMMEDIATELY XMITTED TO THE ACFT HOLDING ON TXWY A AT TXWY A5; FLT Y; L1011 I THINK; ASKING THEIR INTENTIONS. THEY REPLIED THEY WERE NOT READY. GND IMMEDIATELY GAVE US THESE INSTRUCTIONS. 'FLT X TURN L TO TXWY A4; RPT TURNING ON RWY 5L.' WHEN WE TURNED R ON RWY 5L WE RPTED; 'FLT X ON RWY 5L HDG SW.' TO THIS; GND REPLIED; 'RPT CLRING THE RWY.' 'ROGER.' APPROX 40 SECONDS LATER; GND ASKED 'ARE YOU CLR OF THE RWY?' OUR RESPONSE; 'NO FLT X.' HE ASKED US TO 'EXPEDITE TFC ON AN 8 MI FINAL.' I THEN RPTED PASSING TXWY A7 FOR FURTHER GND SITUATIONAL AWARENESS. TO THIS GND REPLIED; 'FLT X; YOU ARE GOING THE WRONG WAY; EXIT AT TXWY A11 AND HOLD ON TXWY A.' THE RVR CAME UP WITHIN 10 MINS (APPROX) AND WE DEPARTED RWY 5L UNEVENTFULLY WITH NO FURTHER DISCUSSION REGARDING A CONFLICT WITH THE TAXI INSTRUCTIONS. IT WAS OUR UNDERSTANDING THAT GND CTL UNDERSTOOD OUR REQUEST TO CONTINUE THE TAXI TO DEPART RWY 5L. THIS IS BECAUSE OF THE SEQUENCE AND CONTEXT OF THE RADIO XMISSIONS; AND THAT HE ASKED THE ACFT AHEAD OF US IF THEY WERE READY TO CONTINUE; AND THEY WERE NOT. WE THOUGHT THAT GND WAS GOING TO TAKE US AROUND THEM VIA TXWY A4 AND DOWN RWY 5L TO DEPART RWY 5L. AT NO TIME WERE WE GIVEN TAXI INSTRUCTIONS TO RWY 5R. AND AT NO TIME DID WE ASK FOR A RWY 5R DEP. THIS WAS A POTENTIALLY VERY SERIOUS SIT; GND CTL TELLING US TO EXPEDITE A TAXI ON A RWY THAT HE THINKS WE ARE GOING IN THE OPPOSITE DIRECTION ON. THIS SIT COULD HAVE BEEN AVOIDED BY GND CTL TELLING US THAT: 1) HE IS CHANGING OUR RWY OF DEP; AND 2) TELLING US WHAT DIRECTION TO TURN; IE; R OR L ON RWY 5L. WE THOUGHT WE WERE BEING EXTRA VIGILANT IN THE LOW VISIBILITY CONDITIONS; BUT WE COULD HAVE AVOIDED THE CONFUSION BY; INSTEAD OF SAYING WE ARE 'HDG SW ON RWY 5L;' THAT WE WERE TURNING R ON RWY 5L; OR WE ARE BACK-TAXIING ON RWY 5L.