IMO, ATC have no responsibility to provdie you with terrain clearance.
My understanding is: depending on what type of aircraft you are in, the CAO 20.7 series will give you the minimum obstacle clearance required until you reach the cruise eg 35ft above obstacles (50ft if you have to turn) at the performance required eg 2% net with an engine out. If all that's too hard, then you demand a departure from the overhead (or some other direction) to allow youself enough time and track miles to climb up to the appropriate MSA.
Therefore, no need to be at LSALT by 5nm, you only need to be missing the obstacles by 35ft (and tell the GPWS beforehand so it doesn't get excited).