WDB CLRED FOR APCH AND LNDG ON RWY 5R LANDS ON 5L INSTEAD.

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WX WAS MARGINAL. WE WERE CLRED FOR 5R. THEY CUT US IN TIGHT AND HIGH FROM THE L SIDE. AUTOMATIC CAPTURE OF COURSE DIDN'T SEEM TO BE OCCURRING PROPERLY SO THE AUTOPLT WAS DISENGAGED. WHILE DSNDING CONFIGURING; AND CAPTURING THE ILS TO 5R WE BROKE OUT AND SAW THE RWY. WE ENDED UP LNDG ON 5L INSTEAD. THE BASIC PROBLEM FROM OUR STANDPOINT WAS A FAILURE TO STAY ON THE INSTS AFTER WE SAW THE RWY. ONE REASON FOR THIS WAS BECAUSE WHEN WE BROKE OUT WE WERE HIGH ON FINAL AND MISALIGNED SO IT TOOK A FEW CORRECTIONS TO GET BACK ON WHAT WE THOUGHT WAS THE R COURSE. WE WERE HIGH BECAUSE 5L IS DISPLACED BACK FROM 5R. IT TOOK MOST OF OUR ATTN TO MAKE A SAFE LNDG. I AM EXPERIENCED IN THE AIRPLANE AND QUITE FAMILIAR WITH MEXICO CITY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. WHEN THE AUTOPLT WAS DISENGAGED; THEY WENT TO RAW DATA. THEY NEVER DID CATCH THE GS. IF THEY HAD; THEY PROBABLY WOULD HAVE GOTTEN A GPWS WARNING. THEY LANDED LONG ON RWY 5L. ATC HAD THEM ON RADAR DURING THE FULL APCH AND; REALIZING WHAT THEY WERE ABOUT TO DO; ALLOWED THEM TO CONTINUE FOR THE L RWY RATHER THAN CAUSE GREATER DISTR CORRECTING THEM TO THE R ONE. THERE WAS NOTHING WRONG WITH ANY OF THE NAVAIDS.