B737-900 FLT CREW HAS A HDG TRACK DEV DURING THE LAX 5 DEP.

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OUR CLRNC WAS THE LAX 5 (250 DEG HDG TO SMO 160 DEG RADIAL THEN L TURN TO 220 DEGS). WE WERE TO KEEP THE SAAB ACFT AHEAD IN SIGHT AS HE WILL BE TURNING SBOUND. AFTER TKOF WHILE COMPLETING PNF DUTIES; I REALIZE WE ARE TURNING PRIOR TO THE SMO 160 DEG RADIAL. SIMULTANEOUSLY; THE LAX TWR MUST HAVE RECOGNIZED THE EARLY TURN AND ADVISED US TO FLY THE LAX 5 AS PUBLISHED. WE IMMEDIATELY STOPPED OUR TURN AND CONTINUED STRAIGHT OUT. WE WERE HANDED OFF TO SOCAL DEP AND ASKED IF THE TWR HAD GIVEN US AN EARLY TURN. I REPLIED THEY HAD NOT; BUT WHILE MY ATTN WAS DIVERTED I HAD LOST SIGHT OF THE SAAB. SOCAL TOLD US TO STOP OUR CLB; WHICH WE DID. ONCE CLR; WE CONTINUED OUR CLB AND WERE HANDED OFF TO THE NEXT SECTOR. IN DISCUSSING THE EVENTS WITH THE FO; HE TOLD ME HE HAD NEVER LOST SIGHT OF THE SAAB. IT'S HARD TO SAY WHAT CAUSED THIS SITUATION. WE WERE ORIGINALLY ANTICIPATING RWY 24L AND HAD THAT SET IN THE FMC; AS WE TAXIED TO RWY 25R I CHANGED THE RWY IN THE COMPUTER AND MADE SURE THE 160 DEG RADIAL WAS IN THE LEGS PAGE; HOWEVER; WE DID NOT VERBALLY DISCUSS THE PROC AND TURN; AND THIS MAY HAVE CONTRIBUTED TO THE ERROR. BECAUSE THE DEP PROC IS DIFFERENT DEPENDING ON RWYS WE SHOULD HAVE BRIEFED THE PROHIBITION TO THE TURN PRIOR TO THE SMO 160 DEG RADIAL. SUPPLEMENTAL INFO FROM ACN 703299: IN 10 YRS OF FLYING OUT OF LAX; I HAVE DEPARTED ON SBOUND FLTS FROM THE 25 RWYS ROUGHLY 25-30 TIMES. AND IN EACH CASE; IMMEDIATELY AFTER TKOF; CONTRARY TO THE PUBLISHED DEP PROC DIRECTING A TURN AT THE SMO 160 DEG RADIAL AND THE TXWY SIGNAGE PROHIBITING ANY TURNS PRIOR TO THE SHORELINE; HAD BEEN GIVEN THE CLRNC; 'START YOUR TURN NOW; AND CONTACT DEP.' IT'S ALSO VERY COMMON; WHEN OPERATING A SBOUND DEP FROM THE 24 RWYS; TO BE ISSUED A TURN TO 210 DEGS OR 220 DEGS. AND; SIMILARLY; IMMEDIATELY AFTER TKOF; AND WELL BEFORE REACHING THE SHORELINE; IT'S VERY ROUTINE TO BE TOLD TO 'START YOUR TURN NOW.' THIS WAS A CASE OF SOMEONE HEARING WHAT THEY 'EXPECTED' TO HEAR; AND DOING WHAT THEY 'ANTICIPATED' THEY WOULD BE CLRED TO DO. I HAD BRIEFED THE DEP WITH REFS TO THE LAXX 2 CHART REGARDING THE TURN TO 220 DEGS AT THE SMO 160 DEG RADIAL; AND THE TXWY SIGNS STATING 'NO TURNS BEFORE THE SHORELINE.' I ALSO BRIEFED THAT I EXPECTED TO BE CLRED TO START THE TURN WELL BEFORE THE RADIAL. I HAD THE 160 DEG RADIAL DEPICTED ON MY MAP; BUT STARTED THE TURN EARLY ANTICIPATING THE CLRNC I HAD ALWAYS RECEIVED IN THE PAST.