A320 FLC CROSSED RWY 5L AT MMMX WITHOUT ATC APPROVAL AS ANOTHER TAKES OFF.

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THE CAPT WAS THE PF AND I WAS PERFORMING THE PNF DUTIES. WE HAD JUST LANDED ON RWY 5R AT MEXICO CITY. AS WE APCHED TXWY FOXTROT; TWR TOLD US TO TAKE TXWY FOXTROT AND TO CROSS RWY 5L. AT THAT MOMENT; I WAS CONFIDENT THAT WAS THE CLRNC AND DID NOT QUESTION IT. I READ THE CLRNC BACK AS; 'TAKE TXWY FOXTROT AND CROSS RWY 5L.' I THEN LOOKED OUT MY WINDOW TO LOOK FOR TFC; AND THEN TOWARDS THE CAPT'S WINDOW. THE ANGLE OF TXWY FOXTROT MAKES IT DIFFICULT TO SEE ALL THE WAY DOWN THE RWY; ESPECIALLY FROM THE R SEAT. I SAW THAT THE CAPT HAD JUST LOOKED OUT HIS WINDOW AND THEN LOOKED FORWARD TO CROSS RWY 5L. ONCE CLR OF THE RWY; I SAW FROM THE L; AN ACFT XING BEHIND US. IT WAS THEN THAT TWR TOLD US WE WERE TO HAVE HELD SHORT OF RWY 5L ON TXWY F. I FOUND THIS VERY PUZZLING; FOR I READ BACK THE CLRNC TO CROSS RWY 5L WITH NO CORRECTION. I HAD NO REASON TO BELIEVE WE WERE TO HOLD SHORT. SOME OF THE CIRCUMSTANCES THAT MAY HAVE LED TO THIS WERE; OF COURSE; THE LANGUAGE BARRIER. I MUST HAVE MISSED HIS CLRNC TO HOLD SHORT. THE CTLR ALSO MISSED MY READBACK TO CROSS RWY 5L. ALSO; THE ANGLE OF THE TXWY ACCOMPANIED BY THE NUMEROUS LIGHTS ON VEHICLES; ETC; WHILE AT THE SAME TIME POOR ARPT LIGHTING MAKES IT HARD TO SEE OBJECTS; ESPECIALLY AT NIGHT. IF I HAD THOUGHT THE CLRNC WAS CONFUSING; I WOULD HAVE ASKED THE CTLR TO REPEAT IT. SUPPLEMENTAL INFO FROM ACN #568125: I WAS CONCERNED ABOUT HOT BRAKES; BECAUSE OF THE HIGH ELEVATION AT MEX; SO I LET THE ACFT ROLL RIGHT DOWN FOXTROT AS TO CLR RWY 5L AS QUICKLY AS POSSIBLE AND STAY OFF THE BRAKES. ABOUT 3/4 OF THE WAY ACROSS RWY 5L; I SAW AN ACFT APCHING. I QUICKLY EXITED THE RWY AND WAS ON TXWY BRAVO AS THE ACFT FLEW PAST. IT WAS AT THIS POINT THAT THE TWR NOTIFIED US THAT WE WERE TOLD TO HOLD SHORT OF RWY 5L. AFTER THINKING ABOUT THIS SIT; I CONCLUDED THAT SEVERAL FACTORS CONTRIBUTED TO THIS INCIDENT. FIRST AND FOREMOST IS THE LANGUAGE PROB COUPLED WITH NIGHT TIME; WHICH LED TO OUR LACK OF SITUATIONAL AWARENESS OF THE ACFT TAKING OFF RWY 5L. THE LANGUAGE BARRIER ALSO LED TO US NOT FULLY UNDERSTANDING ATC CLRNC TO HOLD SHORT; AND ALSO THE TWR NOT HEARING OUR READBACK. IN THE FUTURE; IF I MISS ANY PART OF THE CLRNC; I WILL HAVE IT VERIFIED. THE ANGLE OF THE RWY TO TXWY F MADE IT DIFFICULT TO SEE THE APCH END OF TXWY L.