Some new RBIBDs with block size 5 and PBDs with block sizes ≡1 mod 5

(v,5, 1) RBI BDs were known to exist for all but 109 values of v == 5 mod 20. Solutions are given for all but 6 of these. Also given is a new (45,5,3) RBIBD plus some new incomplete TDs, 14 new (v,6,1) BIBDs and some new PBDs with K = {6} u {Prime powers == 1 mod 5}. A design is a pair (X,5l) where X is a finite set (whose elements are called paints) and .9[ is a collection of subsets of X (called blocks). A group divisible design (GDD), denoted by GD(K, A, G, '" is a design on v points, divided into groups with sizes from G, and block sizes from K such that two points appear together in A blocks if in different groups, and in no blocks if in the same group. The parameter A is called the index of such a design. Also, if K = {k} or G = {g}, we sometimes write kfor {k} and 9 for {g}. A pairwise balanced design (a (v, K, A) PBD) is a GO(K, A, 1, "'; if the block size is uniform, with K = {k}, then such a PBO is called a balanced incomplete block design, (a (v, k, A) BIBO). A transversal design, denoted TD(k, '" is a GD({k}, 1, {v}, k0.