Yes, it will - be in no doubt about that. Obviously, with the current crisis, the announcement has been delayed, but there will be a T5 at Heathrow and don't be at all surprised if LHR is given a third runway as well; there would be hell to pay of course, but there is actually some space north of the airport.
It would require knocking down a few homes, not that it is a decision that should be taken lightly, but LHR is the most important economic engine in the UK and hopefully, the PM will use the kudos he has built up in the current situation to back this. It would be a great help to the country's major airlines in the growth plans to be able to have a third runway - even a short one (as it would be) of about 7,000'. This would take pressure off the current runways and allow more feeder flights.
Both the airlines and the London Chamber of Commerce have spoken in favour of this.