the 2 isometry classes of irreducible [5,2,3]_3 codes are:

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

code no       2:
================
1 1 1 2 0
2 1 0 0 2
the automorphism group has order 12
and is strongly generated by the following 4 elements:
(
2 0 0 
0 2 0 
1 1 1 
, 
1 0 0 
1 2 0 
0 0 2 
, 
0 2 0 
2 0 0 
0 0 2 
, 
1 2 0 
1 0 0 
0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4), 
(2, 5), 
(1, 2), 
(1, 2, 5)
orbits: { 1, 2, 5 }, { 3, 4 }