SMA MISUNDERSTANDS CLB CLRNC; HAS NMAC.

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THE PROB AROSE WHEN TWR CLRED ME TO CHANGE HDG AND CLB TO ASSIGNED ALT OF 5000 FT. (THIS WAS MY UNDERSTANDING) I WAS HANDED OFF TO DEP AT WHICH POINT THEY CLRED ME TO 4000 FT. I DON'T REMEMBER THE 4000 FT CLRNC AND INSTEAD CLBED TO 5000 FT. ANOTHER ACFT (A 4 ENG TURBOPROP 'ELECTRA') CROSSED FROM R TO L IN FRONT OF ME AT 5000 FT. I HAD VISUAL CONTACT WITH THE OTHER ACFT PRIOR TO REACHING 5000 FT AND AS IT CROSSED IN FRONT OF ME. I PASSED BEHIND THE 'ELECTRA' WITHOUT HAVING TO PERFORM EVASIVE MANEUVERS. I WOULD ESTIMATE WE CAME WITHIN 500 FT OF EACH OTHER. I BELIEVE SEVERAL FACTORS CONTRIBUTED TO THIS. I WAS FLYING AN ACFT RELATIVELY NEW TO ME. I HAD 7.1 HRS DUAL IN THAT ACFT AND THIS WAS MY 1ST FLT IN THAT ACFT ALONE. JUST PRIOR TO THIS TKOF; I HAD TAKEN OFF AND THE COCKPIT DOOR HAD OPENED IN FLT. THIS NECESSITATED A LNDG TO CLOSE AND SECURE THE DOOR. ON THE SECOND TKOF AND CLBOUT; THE INCIDENT OCCURRED. I BELIEVE I MUST HAVE MISCOMMUNICATED WITH ATC ABOUT ALT CLRNC BECAUSE OF THOSE FACTORS. TO PREVENT ANY RECURRENCE ON MY PART OF MISCOMMUNICATING CLRNCS; I WILL NOTE ALL ALT AND HDG CHANGES ON A KNEE BOARD. I HAVE RENEWED THE PLTS OPERATING HANDBOOK FOR ALL SYS AND EMER SITS. I HAVE SCHEDULED ADDITIONAL DUAL TIME TO PERFORM APCHS UNDER SIMULATED INST CONDITIONS. I BELIEVE ATC SHOULD HAVE GIVEN BETTER HORIZ SEPARATION BTWN ACFT. I BELIEVE ATC SHOULD HAVE RECOGNIZED THE 2 ACFT WERE ON COURSE TO BE WITHIN 500 FT OF EACH OTHER AND GIVEN INSTRUCTIONS TO CHANGE HDG.