PDF export is fundamentally different from bitmap export.
When exporting to PDF (or printing), a lineweight of 1mm means that a line is exported (or printed) as 1mm wide on paper (regardless of the drawing scale used). In your case, the drawing scale is 1:5, so a 1mm thick line is 1mm thick on paper, but 5mm in drawing units.
When exporting to a bitmap, there is no absolute paper size. The width of a bitmap in Millimeters is a matter of interpretation (not bearing in mind formats which support a resolution). For bitmaps, lineweights are exported in drawing units. I.e. a 1mm thick line is as thick as a 1mm long line is long.
Layer states offer a potential solution:
https://qcad.org/tutorial-working-with-layer-states
Another way to make them look the same would be to export your PDF 1:1 to a larger page size.