Indeed. RRK is right about the tubes not being electrically compatible with each other.
There are some conversion kits that have an integrated ballast that will allow you to convert a F32T8 fluorescent tube fixture to use F28T5 HE fluorescent tubes. As a matter of fact, I have actually imported some conversion kits from the UK that can convert a F40T12 preheat fluorescent tube fixture to F28T5 HE.
https://www.lighting-gallery.net/gallery/displayimage.php?album=6271&pos=31&pid=211568https://www.lighting-gallery.net/gallery/displayimage.php?album=6271&pos=30&pid=211601By the way, here is a F32T8 to F28T5 conversion kit that should suit your needs:
https://www.ebay.com/itm/143192829219Another alternative is to swap the ballasts while you use the T8 to T5 adapters.