FLC OF AN MLG ACR ACFT INADVERTENTLY STARTED A VISUAL APCH TO THE WRONG ARPT.

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WE WERE ENRTE FROM CLT; NC; TO TRI; TN. WE WERE AT APPROX 10000 AND GIVEN ARPT AT 1 O'CLOCK AND TOLD WE WERE BEING VECTORED FOR A VISUAL APCH TO RWY 5. AT THE TIME THE CTLR CALLED POS OF ARPT WE LOOKED OUT AND JUST CAUGHT THE END OF RWY BELOW. WE CALLED ARPT IN SIGHT AND WAS GIVEN CLRNC FOR A VISUAL APCH TO RWY 5 WITH A R BASE SO I STARTED TO DSND. I WAS POSITIONING AIRPLANE FOR A R BASE; WE HAD GOOD GND CONTACT AT ALL TIMES. AT THE TIME I WAS STARTING A TURN FOR BASE LEG THE CTLR TOLD US THAT HE HAD A LOW ALT ALERT AND TO CLB TO 5300 FT; WHICH WE DID. AT THAT TIME WE REALIZED THAT WE WERE STARTING THE APCH TO THE WRONG ARPT. IF WE HAD CONTINUED WHEN WE TURNED BASE AND SAW ARPT; WE WOULD HAD KNOWN IT WAS THE WRONG ONE; BUT IT WAS BEHIND US FOR THE WHOLE TIME WE WERE ON APCH. WE WOULD HAVE ALSO KNOWN IT WAS WRONG WHEN WE TURNED BASE BECAUSE WE HAD LOC FOR 23 SET IN. WE WERE NEVER IN ANY DANGER AND WOULD NOT HAVE LANDED AT WRONG ARPT; BUT WE SHOULD HAVE BEEN MORE AWARE OF OUR POS AND THE CTLR COULD HAVE CALLED US SOONER. HE SHOULD HAVE NOTICED THAT I WAS FLYING A DOWNWIND TO OTHER ARPT.