Kramer and Magliveras constructed simple 5-(24, 8, λ) designs for λ ≤ 9. Betten et al. constructed simple 5-(24, 8, λ designs for λ = 16, 17, ..., 484. In this paper, we construct 15 mutually disjoint Steiner systems S(5, 8, 24) and thus we construct simple 5-(24, 8, λ) design for λ = 10, 11, 12, 13, 14 and 15. As a consequence there exists a simple 5-(24, 8, λ) design for any positive integer λ ≤ λmax = 969. © 2003 Elsevier Science (USA). All rights reserved.