a = PermutationGroupElement('(1,2)')
b = PermutationGroupElement('(1,2,3,4,5)')
e = PermutationGroupElement('()')
S = [a,b, b.inverse()] #generators, closed under inverses
S5 = PermutationGroup(S)
G = S5.cayley_graph(generators=S)
p = G.shortest_path(V[0], V[1])
genterms = [p[i+1] * p[i].inverse() for i in range(len(p)-1)]
print("vertices on shortest path: n" + str(p))
print("generators on shortest path: n" + str(genterms))

Output:

vertices on shortest path:
[(), (1,2,3,4,5), (1,3,5,2,4), (1,3,5)(2,4), (1,2,3,4), (4,5)]
generators on shortest path:
[(1,2,3,4,5), (1,2,3,4,5), (4,5), (1,4,5,3,2), (1,4,5,3,2)]