Hopefully Genius1 or xxxxx happen to be reading this. They seem to know a lot about the inner workings of LHR.
Perhaps the tunnel does continue under the terminal but is currently sealed off and the ramp up to 5C is a tunnel within a tunnel (a bit like the Strand Underpass is built within some old tramway tunnels), but doing this seems more effort than it's worth even though they probably knew T5D would be a long time coming.