Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$

J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue $\leq t$ for a given positive integer $t$. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with non-principal eigenvalue $t$ for $t=1,2,\dots$ In the article by A. K. Gutnova and A. A. Makhnev "Extensions of pseudogeometrical graphs for $pG_{s-4}(s,t)$" the Koolen problem was solved for $t=4$ and for pseudogeometrical neighborhoods of vertices. In the article of A. A. Makhnev “Strongly regular graphs with nonprincipal eigenvalue 5 and its extensions” the Koolen problem for $t=5$ was reduced to the case where the neighborhoods of vertices are exceptional graphs. In this paper intersection arrays for distance-regular graphs whose local subgraphs are exceptional pseudogeometric graphs for $pG_{s-5}(s,t)$.