AN MD80 CREW MISUNDERSTOOD A TAXI CLRNC AT MMMX; TURNED THE WRONG WAY AND TAXIED ONTO A RWY NOT CLRED TO BE ON.

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LANDED FLT XX ON RWY 5R. PARKED ON RAMP SPOT; THEN TOWED TO GATE AFTER PAX OFFLOAD. 1 HR LATER; WE DEPARTED AS FLT XY; PUSHED BACK ONTO RAMP S OF THE TERMINAL FACING S. ATIS INFO INDICATED RWY 5R IN USE. CALLED GND CTL FOR TAXI ; CLRED INTXN B TO RWY 23L. I REQUESTED THE WINDS; REPLY WAS 200 DEGS AT 8 KTS. WE CONSIDERED OURSELVES TO BE ON TXWY C AND AGREED ON THE RTE AFTER NOTICING A YELLOW TXWY SIGN WITH BLACK LETTERING INDICATING INTXN B AHEAD. CAPT TAXIED STRAIGHT AHEAD AND TO THE L DOWN WHAT WE BELIEVED TO BE BRAVO. MEANWHILE; I WAS DISTR CALLING CLRNC DELIVERY FOR AN AMENDED CLRNC TO DEPART RWY 23L. THE CAPT THEN NOTICED WE WERE ON RWY 23R HDG E. I IMMEDIATELY NOTIFIED GND CTL WHO ISSUED 180 DEG TURN ON RWY 23R TO B7 THEN B TO HOLD SHORT RWY 23R. LUCKILY; RWY 23R WAS NOTAMED CLOSED. UPON EXITING RWY 23R AT B7; WE NOTICED THAT THERE WAS NO RWY IDENT EXCEPT A BADLY SOILED AND POORLY PAINTED HOLD SHORT MARKINGS ON THE TXWY. ALSO; THE YELLOW TXWY B INTXN MARKER ON THE EDGE OF RWY 23R/5L. I BELIEVE THAT THE RELOCATION OF THE AIRPLANE COMBINED WITH THE NONSTANDARD ICAO ARPT MARKINGS; COUPLED WITH MY DISTRS CALLING FOR CLRNC ABOUT RWY CHANGE; LED TO THIS RWY INCURSION. SUPPLEMENTAL INFO FROM ACN 517734: I THOUGHT THAT WE WERE ON TXWY C; SO I TURNED R TO TAXI TO TXWY B SINCE THERE WAS SIGNAGE SHOWING TXWY B TO OUR R AND NO RWY SIGN TO INDICATE RWY 23R. I THINK MY CONFUSION STARTED WHEN WE PARKED AT SPOT XX WHICH IS NEXT TO TXWY C. BUT; WHILE WE WERE THERE; THE ACFT WAS MOVED TO GATE YY BY MEX CITY GND CREWS.