I would like to create a vector from my DEM raster so that it looks like the example I attached as an image. I want the altitude levels of the Alps in Austria to be represented in 5 different color gradations. I tried to make a vector out of the raster using "Contour" tools, but I don't want to create contour lines. Does anyone have an idea how to do it?
Instead of contour lines, create contour polygons: Menu Processing > Toolbox > Contour Polygons(see QGIS documentation).
It is a tool provided by GDAL library, needs GDAL 2.4.0 or higher (should be the case in newer QGIS versions), see here for details. For older versions, GRASS tool
r.recode or even raster calculator would be an alternative, see here.