the 2 isometry classes of irreducible [5,2,3]_5 codes are:

code no       1:
================
1 1 1 4 0
1 1 0 0 4
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
2 0 0 
0 2 0 
3 3 3 
, 
0 2 0 
2 0 0 
0 0 2 
, 
3 3 3 
0 0 2 
2 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4), 
(1, 2), 
(1, 3, 2, 4)
orbits: { 1, 2, 4, 3 }, { 5 }

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