Intriguing sets of W(5,q)W(5,q), q even

Infinite families of (q+1)(q+1)-ovoids and (q2+1)(q2+1)-tight sets of the symplectic polar space W(5,q)W(5,q), q   even, are constructed. The (q+1)(q+1)-ovoids arise from relative hemisystems of the Hermitian surface H(3,q2)H(3,q2) and from certain orbits of the Suzuki group Sz(q)Sz(q) in his projective 4-dimensional representation. The tight sets are closely related to the geometry of an ovoid of W(3,q)W(3,q). Other constructions of sporadic intriguing sets are also given.