All your pages are in one spread. You can't export just part of the spread as "spread".
Does this mean I should be selecting "pages" instead of spread when I try to export range 2-4?
Yes, but then you got separate pages.
If you want pdf with "spread" of 2-4 pages, you need them to be a spread in InDesign, too. Take pages 1 and 5 to separate spreads. Then export spread, containing your pages 2-4.
... or sometimes you can find it's less hassle just to crop your "wide" spread after export, directly in Acrobat.
Not so good workflow, but in this particular case it would work...