Why doesnt vegetation grow in mountains?

Question

I think it has something to do with the temperature and how vegetation grows at a temperature of 5 degrees celcius and when you go higher the temperature drops below that

is that right?

Answer 1

tree line is the term for the altitude at which trees can no longer survive.  not an actual line, but a gradual decline as  altitude increases.  lower temperatures and less moisture are the main reasons

Answer 2

What do you mean by vegetation?  Although there will be a zone above which trees are stunted or absent, there is alpine tundra with a layer of permafrost beneath the surface.  Grasses, various flowering plants, mosses and lichens all can grow above the timber line.  Even bare rocks will harbor lichens and mosses.

Temperature, thin soil, high winds, solar radiation are all factors in limiting growth above the timber line.