The safe way would to be using a real CSV parser:

use Text::CSV_XS qw( csv );

my @sorted = sort {
    $a->[5] cmp $b->[5] ||
    $a->[4] cmp $b->[4]
    } @{csv (in => "sorted.csv")};
csv (out => "sorted.csv", in => \@sorted);
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Which could be shortcutted to

csv (in  => [ sort { $a->[5] cmp $b->[5] ||
                     $a->[4] cmp $b->[4]
                     } @{csv (in => "sorted.csv")}],
     out => "sorted.csv");
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