Block-transitive \(2-(v,5,\lambda)\) designs with sporadic socle

<p>This paper contributes to the classification of non-trivial <span class="math inline">\(2\)</span>-designs with block size <span class="math inline">\(5\)</span> admitting a block-transitive automorphism group. Let <span class="math inline">\({\cal D=(P,B)}\)</span> be a non-trivial 2-<span class="math inline">\((v,5,\lambda)\)</span> design and <span class="math inline">\(G\)</span> be a block-transitive automorphism group of <span class="math inline">\(\mathcal{D}\)</span>. The main aim of this paper is to determine all pairs <span class="math inline">\((\mathcal{D},G)\)</span> when Soc(<span class="math inline">\(G\)</span>) is a sporadic simple group.</p>