Puzzle #178 - Glass Houses (Liar Skyscrapers)

So. It turns out that Liar Skyscrapers was actually possible to construct for a 5x5. I almost can't believe that this works or that I managed to do so. Solve as a normal Skyscrapers puzzle, except every number is lying and should actually be a different number. So a 2 can see 1, 3, 4 or 5 numbers, but never 2.

puzz.link interface      penpa interface

Thanks to Deusovi, TGE and edderiofer for testsolving this- it took a couple tweaks to fix but it was possible to fix.