the 1 isometry classes of irreducible [5,1,5]_5 codes are:

code no       1:
================
1 1 1 1 4
the automorphism group has order 120
and is strongly generated by the following 6 elements:
(
3 0 0 0 
0 3 0 0 
0 0 3 0 
2 2 2 2 
, 
3 0 0 0 
0 3 0 0 
0 0 0 3 
0 0 3 0 
, 
1 0 0 0 
0 1 0 0 
4 4 4 4 
0 0 1 0 
, 
1 0 0 0 
0 0 1 0 
0 1 0 0 
0 0 0 1 
, 
0 0 0 1 
1 0 0 0 
0 0 1 0 
0 1 0 0 
, 
2 2 2 2 
0 0 3 0 
0 0 0 3 
0 3 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5), 
(3, 4), 
(3, 4, 5), 
(2, 3), 
(1, 2, 4), 
(1, 5)(2, 4, 3)
orbits: { 1, 4, 5, 3, 2 }