On Resolvable BIBDs with Block Size Five

It is shown that a resolvable BIBD with block size five and index two exists whenever \(v \equiv 5 \pmod{10}\) and \(v \geq 50722395\). This result is based on an updated result on the existence of a BIBD with block size six and index unity, which leaves \(88\) unsolved cases. A construction using difference families to obtain resolvable BIBDs is also presented.