A UNITED STATES BASED ACR MLG PERFORMS AN UNAUTH RWY XING AT MEXICO CITY CAUSING A DC9 ON TKOF TO ABORT HIS TKOF.

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DURING ROLLOUT AFTER LNDG ON RWY 5R AT MEXICO CITY; WE RECEIVED INSTRUCTIONS FROM THE TWR. AT THE TIME; WE WERE USING REVERSE THRUST AND THE COCKPIT ENVIRONMENT WAS VERY NOISY. MY UNDERSTANDING WAS THAT WE WERE CLRED TO TURN L (OFF OF RWY 5R) AND CROSS RWY 5L. I READ BACK THOSE INSTRUCTIONS AND WE CROSSED RWY 5L. THERE WAS CONVERSATION IN SPANISH AFTER WE RECEIVED OUR INSTRUCTIONS. WHEN WE CHANGED TO GND FREQ; WE WERE ASKED TO RETURN TO TWR FREQ. TWR INFORMED US THAT WE HAD CROSSED RWY 5L WITHOUT CLRNC AND THAT A DC9 HAD ABORTED HIS TKOF. WE WERE THEN CLRED TO GND AND TAXIED IN TO OUR GATE. SUPPLEMENTAL INFO FROM ACN 422706: AFTER THE ACFT CAME TO A SAFE TAXI SPD AND IN A QUIETER ENVIRONMENT; I DISCUSSED THE CLRNC AGAIN WITH THE FO TO CONFIRM WE WERE TO CROSS RWY 5L. ALTHOUGH TXWY E HAS AN EXTREME ANGLE; I FELT SURE NO ONE WAS ON RWY 5L. BUT AGAIN; IT WAS VERY HARD TO SEE THE FAR END OF THE RWY AT THAT ANGLE. THE CLRNC WAS ONLY HEARD BY THE PNF AND WHEN THIS OCCURS A SECOND XMISSION SHOULD BE REQUIRED.