A TFC CONFLICT RESULTS FROM AN INCORRECT READBACK AND UNDERSTANDING OF A DSCNT CLRNC THAT WAS NOT CAUGHT BY THE CTLR.

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ENRTE FROM LGB TO SBA. WITHIN APPROX 10 MINS FROM TKOF; WE WERE GIVEN A CLB CLRNC TO 10000 FT AND DIRECT TO WANG INTXN. AFTER PROCEEDING TOWARD WANG INTXN; THE SOCAL CTLR GAVE A DSCNT CLRNC (AS HEARD BY CREW) TO 5000 FT. PNF RESPONDED TO CLRNC FROM SOCAL; 'DSCNT TO 5000 FT' AND SET 5000 FT IN ALT SELECTOR. AFTER PNF SET 5000 FT INTO THE ALT SELECTOR; PF STATED 'DSCNT TO 5000 FT' AND BEGAN A SLOW DSCNT DUE TO A CRUISING AIRSPD OF 300 KIAS. AFTER DSCNT HAD BEGUN; PNF CHANGED SECONDARY RADIO OVER TO SBA ATIS FREQ FOR WX. SOCAL GAVE US A FREQ CHANGE TO SBA APCH THAT PF RESPONDED TO AND SWITCHED PRIMARY FREQ. WHILE LISTENING; PF CONTINUED TO DSND AS PF PICKED UP ACFT AT ABOUT 5-8 MI AT HIS 2 O'CLOCK POS ON TCASII AND VISUALLY. THE 1 ACFT THAT PF PICKED UP VISUALLY APPEARED TO BE IN A BANK TOWARDS OUR ACFT. DURING THIS TIME; PNF HAD SWITCHED OVER TO FBO FREQ WITH THE SECONDARY RADIO AND BEGAN TALKING TO THEM; PF RECALLS PNF'S PORTION OF THE CONVERSATION BLEEDING OVER HIS HEADSET WITH HIS SELECTION ONLY BEING PRIMARY FREQ. WATCHING THE TFC; WHICH PF RECALLS POINTING OUT TO PNF; HE SLOWED HIS DSCNT RATE. OUR ACFT WAS BELOW 8000 FT WHEN WE THEN RECEIVED A TA AT A HORIZ DISTANCE OF APPROX 2 MI AND THEN AN RA WHICH CALLED FOR A CLB. (OUR LOWEST ALT THAT PF RECALLS WAS 7200-7300 FT?) PF RESPONDED TO THE RA WHILE PNF CONTACTED APCH AND TOLD THEM THAT WE WERE RESPONDING TO A TCASII RESOLUTION. THE CTLR TOLD US TO LEVEL OFF AT 8000 FT; WHICH PNF SET IN THE ALT SELECTOR. PF HAD ALREADY CLBED TO APPROX 8300 FT AND THEN DSNDED BACK TO 8000 FT TO MAINTAIN THAT ALT. SBA APCH ASKED US WHAT ALT WE WERE DSNDING TO INITIALLY AND PNF TOLD HIM THAT WE HAD BEEN DSNDING TO A CLRED ALT OF 5000 FT. SBA APCH CTLR COMMENTED THAT SOCAL NORMALLY DOES NOT PROVIDE CLRNC BELOW 9000 FT IN THE HDOF. VECTORS AND DSCNT WERE THEN GIVEN TO A VISUAL APCH TO SBA. NO FURTHER INCIDENT. APPROX 2 HRS AFTER INCIDENT; THE PNF CONTACTED BOTH SBA APCH AND SOCAL APCH FOR FURTHER INFO AND GUIDANCE. THE INFO THAT WE RECEIVED WAS THAT THE ATC TAPES WERE CHKED AND SHOWED THAT THE SOCAL CTLR HAD GIVEN US A DSCNT CLRNC TO 9000 FT; WHICH PNF HAD RESPONDED TO AS 5000 FT. THE CTLR FAILED TO CATCH THE INCORRECT RESPONSE RESULTING IN A POTENTIAL VIOLATION FOR HIM AND THE PLTS FAILED TO HEAR THE CORRECT DSCNT ALT CLRNC RESULTING IN A POTENTIAL VIOLATION TO THEM. THE RESULTING TA WAS VERIFIED AS A DISTANCE OF 500 FT BTWN THE OTHER ACFT AT 7200 FT AND OUR ACFT AT 7700 FT. LOOKING FOR CONTRIBUTING FACTORS WITH THE INCIDENT; BOTH PF AND PNF WERE WELL RESTED FROM THE NIGHT BEFORE AND WERE NOT IN A RUSH; VMC DAY; WHILE SOCAL TFC IS ALWAYS BUSY; WE WERE VECTORED OVER THE OCEAN WHERE IT WAS NOT EXTREMELY BUSY AS PF RECALLS. THE NEW HEADSETS BEING TRIED OUT FOR A THIRD FLT IN A ROW WERE AN IRRITANT WHEN CREW WAS XFERRED OVER TO SBA APCH BUT PF DOES NOT THINK THEY WERE A FACTOR WITH THE INITIAL DSCNT MISTAKE. HAD THE DSCNT CALL NOT BEEN MISSED; THIS INCIDENT WOULD NOT HAVE OCCURRED NOR WOULD HAVE IT OCCURRED IF THE CTLR HAD CAUGHT OUR READBACK OF 5000 FT INSTEAD OF THE 9000 FT THAT HE GAVE US. PF DOES NOT KNOW IF THE TAPES SHOW THE CTLR GIVING THE DSCNT ALT AS 'NINE' OR 'NINER' THOUSAND FT.