The hyperplanes of DW(5, 2h) which arise from embedding

We show that there are 6 isomorphism classes of hyperplanes of the dual polar space ∆ = DW (5, 2h) which arise from the Grassmannembedding. If h ≥ 2, then these are all the hyperplanes of ∆ arising from an embedding. If h = 1, then there are 6 extra classes of hyperplanes as has been shown by Pralle [23] with the aid of a computer. We will give a computer free proof for this fact. The hyperplanes of DW (5, q), q odd, arising from an embedding will be classified in the forthcoming paper [8].