the 1 isometry classes of irreducible [5,1,5]_27 codes are:

code no       1:
================
1 1 1 1 2
the automorphism group has order 360
and is strongly generated by the following 6 elements:
(
26 0 0 0 
0 26 0 0 
0 0 26 0 
0 0 0 26 
, 1
, 
16 0 0 0 
0 16 0 0 
0 0 16 0 
23 23 23 23 
, 0
, 
2 0 0 0 
0 2 0 0 
0 0 0 2 
0 0 2 0 
, 1
, 
2 0 0 0 
0 0 0 2 
0 2 0 0 
0 0 2 0 
, 2
, 
0 0 3 0 
0 3 0 0 
0 0 0 3 
3 0 0 0 
, 0
, 
6 6 6 6 
3 0 0 0 
0 0 0 3 
0 3 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(4, 5), 
(3, 4), 
(2, 3, 4), 
(1, 4, 3), 
(1, 2, 4, 3, 5)
orbits: { 1, 3, 5, 4, 2 }