the 1 isometry classes of irreducible [5,1,5]_25 codes are:

code no       1:
================
1 1 1 1 4
the automorphism group has order 240
and is strongly generated by the following 8 elements:
(
8 0 0 0 
0 8 0 0 
0 0 8 0 
0 0 0 8 
, 1
, 
22 0 0 0 
0 22 0 0 
0 0 22 0 
8 8 8 8 
, 0
, 
9 0 0 0 
0 9 0 0 
0 0 0 9 
0 0 9 0 
, 0
, 
8 0 0 0 
0 8 0 0 
22 22 22 22 
0 0 0 8 
, 0
, 
20 0 0 0 
0 0 20 0 
0 0 0 20 
0 20 0 0 
, 1
, 
22 0 0 0 
8 8 8 8 
0 0 22 0 
0 0 0 22 
, 0
, 
0 0 0 12 
0 0 12 0 
12 0 0 0 
0 12 0 0 
, 0
, 
10 10 10 10 
0 0 15 0 
0 15 0 0 
15 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(4, 5), 
(3, 4), 
(3, 5), 
(2, 4, 3), 
(2, 5), 
(1, 3, 2, 4), 
(1, 4, 5)(2, 3)
orbits: { 1, 4, 5, 3, 2 }