FA20 CREW HAD A TXWY INCURSION AT DFW.

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EVENT OCCURRED AT DFW ARPT; LANDED ON RWY 17C OUT OF AN ILS; TURNED OFF RWY; ON TXWY M3 AND WAS INSTRUCTED BY TWR TO TURN R ONTO TXWY EL AND HOLD SHORT OF RWY 17R; WHICH I DID. AT THAT POINT; I WAS TOLD TO CROSS RWY 17R AND CONTACT GND CTL; WHICH I DID. WE WERE THEN TOLD TO TURN L ONTO TXWY L AND HOLD SHORT OF TXWY B. AT THAT POINT; I TURNED L TOO FAR AND ENDED UP ON TXWY L4 AND WAS TOLD BY GND CTL THAT WE WERE ABOUT TO ENTER RWY 17R AND TO STOP; WHICH I DID. WE WERE THEN TOLD TO TURN L 45 DEGREES AND PROCEED TO THE NEXT INTXN; WHICH I DID. WE WERE THEN TOLD TO STOP AGAIN; THAT WE WERE STILL ON TXWY L4. WE WERE THEN TOLD TO PROCEED TO TXWY L5 AND RE-ENTER TXWY L AT L5 AND TURN LEFT ON TXWY L TO HOLD SHORT OF TXWY B; WHICH I DID. WE WERE THEN TOLD TO TURN R ONTO TXWY B AND CROSS THE BRIDGE; CONTACT GND ON 121.85; AND TAXI TO GA TERMINAL AT TXWY HA; WHICH I DID. DUE TO THE RAIN ON THE WINDSHIELD; I INADVERTENTLY TAXIED ONTO TXWY L4 INSTEAD OF TXWY L. PLEASE NOTE ON THE ATTACHED ARPT TAXI CHART; THAT THE AREA MARKED IN RED INK WAS THE RTE I FOLLOWED.