Nick,
With your departure clearance you are issued an altitude, normally 5000ft in the case of Sydney.
The SID itself, as Will has said, doesn't have any altitude restrictions (only some conditional altitudes for track changes). This means that the only limitation to your climb is whatever ATC tells you.
So, preflight (or just prior to takeoff) you are cleared to maintain 5000ft. After you take off, you will contact Departures, who will either say maintain 5000, or climb to another level (say FL260). If they say "cancel speed restriction", that has no impact on the altitude they have cleared you to... you must maintain the assigned altitude (which is by ATC in this case), until you are specifically cleared higher.
So, basically, without a specific restriction you do climb, however ATC will ALWAYS give you a clearance limit, even if it is to climb to your cruise altitude.
Edited to add - You might be getting confused with a clearance to CLIMB above a SID clearance limit. This is a bit of an oddity, in that if you have a SID restriction to maintain 5000ft until a waypoint, but ATC say "climb FL260", then you can ignore the SID restriction and climb.
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