Kneel puny Doomtrooper before the might of the Ezoghoul!
Uh, actually you're not exactly right:
A figure of height 5 can only climb up 4 levels, not 5, providing they have 5 movement points to spend.
Intoxication generally does not facilitate comprehension of game rules.
Unfortunately neither does sobriety.
A figure with 5 height can climb a 5 height cliff, it really is that simple. He'll need six movement points to do it.
Betcha a geek gold I'm right.