This will run in a fraction of a second even for your real 30-char width input using any awk in any shell on every Unix box:
$ cat tst.awk
function mutate(old,lgth, new,i,j) {
for (i=5; i<=lgth; i+=5) {
for (j=1; j<=4; j++) {
new = substr(old,1,i-1) substr("ACTG",j,1) substr(old,i+1)
if ( !seen[new]++ ) {
print new
mutate(new,lgth)
}
}
}
}
{ mutate($0,length($0)) }
$ echo 'AAAAAAAAAAAAAAA' | awk -f tst.awk
AAAAAAAAAAAAAAA
AAAACAAAAAAAAAA
AAAATAAAAAAAAAA
AAAAGAAAAAAAAAA
AAAAGAAAACAAAAA
AAAAAAAAACAAAAA
AAAACAAAACAAAAA
AAAATAAAACAAAAA
AAAATAAAATAAAAA
AAAAAAAAATAAAAA
AAAACAAAATAAAAA
AAAAGAAAATAAAAA
AAAAGAAAAGAAAAA
AAAAAAAAAGAAAAA
AAAACAAAAGAAAAA
AAAATAAAAGAAAAA
AAAATAAAAGAAAAC
AAAAAAAAAGAAAAC
AAAACAAAAGAAAAC
AAAAGAAAAGAAAAC
AAAAGAAAAAAAAAC
AAAAAAAAAAAAAAC
AAAACAAAAAAAAAC
AAAATAAAAAAAAAC
AAAATAAAACAAAAC
AAAAAAAAACAAAAC
AAAACAAAACAAAAC
AAAAGAAAACAAAAC
AAAAGAAAATAAAAC
AAAAAAAAATAAAAC
AAAACAAAATAAAAC
AAAATAAAATAAAAC
AAAATAAAATAAAAT
AAAAAAAAATAAAAT
AAAACAAAATAAAAT
AAAAGAAAATAAAAT
AAAAGAAAAAAAAAT
AAAAAAAAAAAAAAT
AAAACAAAAAAAAAT
AAAATAAAAAAAAAT
AAAATAAAACAAAAT
AAAAAAAAACAAAAT
AAAACAAAACAAAAT
AAAAGAAAACAAAAT
AAAAGAAAAGAAAAT
AAAAAAAAAGAAAAT
AAAACAAAAGAAAAT
AAAATAAAAGAAAAT
AAAATAAAAGAAAAG
AAAAAAAAAGAAAAG
AAAACAAAAGAAAAG
AAAAGAAAAGAAAAG
AAAAGAAAAAAAAAG
AAAAAAAAAAAAAAG
AAAACAAAAAAAAAG
AAAATAAAAAAAAAG
AAAATAAAACAAAAG
AAAAAAAAACAAAAG
AAAACAAAACAAAAG
AAAAGAAAACAAAAG
AAAAGAAAATAAAAG
AAAAAAAAATAAAAG
AAAACAAAATAAAAG
AAAATAAAATAAAAG