my $line = $_; chomp $line;
    my @chunks = unpack "(A5)*", $line;
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Just a side note: what's wrong with

    chomp;
    my @chunks = unpack "(A5)*", $_;
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?

(or else

while (my $line=<DATA>) { ...
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instead.)

Also, more on a stylistic personal preference ground:

    foreach my $i (@chunks) {
    print ">" . $i . "<\n";
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why not

    print ">$_<\n" for @chunks;
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instead?