POTENTIAL GND CONFLICT OCCURS BTWN LNDG TFC AND TAXIING TFC.

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GND TAXIING INCIDENT AT BHM; SEP/XX/95; DC9-10. AT APPROX XA55Z; WHILE TAXIING FROM GATE TO TXWY A AT BHM; AIRLINES FLT; A B727; LANDED AND EXITED RWY 5 AT INTXN A-4 AT A HIGH RATE OF SPD DIRECTLY TOWARD OUR ACFT. I WAS FORCED TO TAKE EVASIVE ACTION CONSISTING OF AN IMMEDIATE L TURN TO STAY SAFELY OUT OF HIS PATH. I QUERIED TWR IF HE HAD CLRED ACR OFF AT THAT EXIT; AND THEY REPLIED THAT THEY HAD NOT AND THAT IT HAD LOOKED CLOSE TO THEM ALSO. I ASKED THE TWR IF THEY WOULD RELAY MY CONCERN TO THE ACR AND THEY ROGERED. I CHKED WITH MY FLT ATTENDANTS TO MAKE SURE EVERYTHING WAS OK IN THE CABIN; CONTINUED OUT TO RWY 5 AND DEPARTED FOR DTW WITH NO FURTHER ACTION TAKEN AT THAT TIME. I LATER FOLLOWED UP WITH A RPT TO NASA ASRS AND THIS NOTE. WX AT THE TIME WAS NOT A FACTOR. THE DISTANCE FROM THE APCH END OF RWY 5 TO INTXN A-4 IS APPROX 8230 FT. LARGELY OWING TO THE FACT THAT MY CREW SAW AN UNSAFE SIT RAPIDLY DEVELOPING AND TOOK TIMELY EVASIVE ACTION; THE INCIDENT WAS NOT SO CLOSE AS TO POSE AN IMMEDIATE; DIRECT HAZARD TO MY ACFT AND PAX. IT WAS; HOWEVER; A VERY UNCOMFORTABLE; UNNECESSARY; AND UNPROFESSIONAL ACTION; BORDERING ON CARELESS AND RECKLESS OP.