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use strict;

...

print "Using <=>:\n", join("\n", sort {$b <=> $a} @dirs), "\n\n";
print "Using cmp:\n", join("\n", sort {$b cmp $a} @dirs), "\n";

Using <=>:
11-09-2004
...
11-09-2004
11-08-2004
11-07-2004