I don't think Bran fell from that TOWER.
Game of Thrones Season 1, Episode 2
Ser Denys Mallister has commanded
the Shadow Tower for 20 years,
Game of Thrones Season 5, Episode 1
in the Tower of the Hand
instead of the Small Council chamber.
Game of Thrones Season 3, Episode 7
Climb to the top of the broken TOWER.
Game of Thrones Season 5, Episode 7
I would now have to climb all the
stairs in the Tower of the Hand?
Game of Thrones Season 3, Episode 7