That should be more than enough time. Including the long walks and waiting for the bus, it should be about 30 minutes max from your gate to T5. Assuming you hit early morning security rush hour at T5, it'll be another 15 minutes or so.

However, that means by the time you get to the lounge it may be as late as 6:30am, after the first wave of early morning arrivals, which may mean you need to wait for a shower (bear in mind they are pretty basic showers, but better than nothing if you need to freshen up ahead of your connecting flight).