A Piper Chieftain (PA31) departed Bankstown on a flight to Moorabbin in accordance with the Instrument Flight Rules. The Sydney Departures controller issued the pilot with radar vectors to intercept the Sydney-Cordo track, together with an instruction to climb to and maintain 5,000 ft. At about that time a Boeing 747 (B747) was approaching Sydney from the west, in instrument meteorological conditions, following a RIVET Standard Terminal Arrival Route. The crew had been issued with a clearance to descend to and maintain 6,000 ft. The flight paths of the two aircraft were to cross each other at approximately right angles, some 8 NM to the south-west of Sydney. The crew of the B747 subsequently advised the Sydney Approach controller that they had received a Traffic Collision and Avoidance System Resolution Advisory (TCAS RA). The RA instruction to climb the aircraft had been followed by the crew and the aircraft reached a maximum altitude of 6,300 ft before returning to the assigned level. At that time the controller observed the radar return of the PA31 descending through 5,300 ft and queried the pilot as to his present level. The pilot replied that he was returning to 5,000 ft. Neither crew sighted the other aircraft. Analysis of recorded radar data revealed there had been a breakdown in separation between the two aircraft. The minimum vertical separation between the B747 and the PA31 was 600 ft whilst the lateral separation was 1.7 NM. The required separation standards were 1,000 ft vertically or 3 NM laterally. The PA31 reached a maximum altitude of about 5,400 ft. The pilot of the PA31 later reported he had been distracted at the time his aircraft was approaching 5,000 ft and had subsequently climbed through his assigned level.