Maximal cocliques in the Kneser graph on point-plane flags in PG(4,q)

We determine the maximal cocliques of size ≥5q2+5q+2 in the Kneser graph on point-plane flags in PG(4,q). The maximal size of a coclique in this graph is (q2+q+1)(q3+q2+q+1).