Your adjacency matrix represents a directed graph. It's possible to go directly from node 2 to node 3 since A(2, 3) is 1 but it is not possible to go directly from node 3 to node 2 since A(3, 2) is 0. The shortest path from 3 to 2 is in fact of length 4: 3 --> 4 --> 5 --> 1 --> 2. Using the graph algorithm functionality introduced into MATLAB in release R2015b:
A=[1 1 0 0 1
1 1 1 0 0
0 0 0 1 0
0 0 1 1 1
1 0 0 0 0];
D = digraph(A);
shortestpath(D, 2, 3) % Returns [2 3]
shortestpath(D, 3, 2) % Returns [3 4 5 1 2]
plot(D) % If you follow the arrows, you have to go around the circle to get from 3 to 2
If you wanted all the edges to be two-way streets, your adjacency matrix would be A|A.'. When I create a graph using that adjacency matrix and ask for the shortest path I get what you're expecting.
G = graph(A|A.');
shortestpath(G, 2, 3)
shortestpath(G, 3, 2)
plot(G) % No arrows. There is an edge you can take in either direction between 2 and 3.
The DISTANCES function for the new graph algorithm functionality is the equivalent of GRAPHALLSHORTESTPATHS for a biograph. The output of DISTANCES for the digraph D agrees with the result you say is incorrect. The output of DISTANCES for the graph G almost agrees with your desired result, but the shortest path from 1 to 4 (and vice versa) is of length 2 not 3 [1 --> 5 --> 4] and the shortest path from 2 to 5 (and vice versa) is of length 2 not 1 [2 --> 1 --> 5.] These paths are easy to see in the plot of G.
