On amply regular graphs with $b_1\le5$

Regular graph of degree $k$ on $v$ vertices such that any edge is contained exactly in $\lambda$ triangles is called edge-regular graph with parameters $(v,k,\lambda)$. Edge-regular graph $\Gamma$ such that $|\Gamma(u)\cap\Gamma(w)|=\mu$ for any two vertices $u$, $w$ with $d(u,w)=2$ is called amply regular graph with parameters $(v,k,\lambda)$. It is obtained the description of amply regular graphs with $k-\lambda-1\le5$.