Crossrail will certainly improve access to LHR, but perhaps not as radically as you expect. On current plans, only 4 Crossrail trains per hour will go to LHR. These won't serve T5. On top of this, likely only 2 per hour from LHR will serve C Wharf (because 50% of Crossrail services going east will go via Stratford, not the Wharf), so passengers will often need to change to get to the Wharf.
Much of this is tied up with access issues on the track into LHR, which is owned by the airport, and they want to preserve "train paths" for their Express services.