Our flight arrives at 15.25 so that solves the dilemma!
we've never managed to get a shower at either T5 galleries lounge. We normally arrive early morning though so that may be the cause although the day we were told they had stopped taking reservations and estimates it would take 9 hours to clear the backlog left us a bit speechless. Not so the passenger behind us who was positively incandescent with rage because with Bronze status he expected some sort of priority.