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my $str = "P H A G E P H A G E P Q K R E P H A G E P W S Q E P H A G E
+ P R D L E P H A G E";

$str =~ s/\s+//g;
my @words = $str =~ /.{1,5}/g;

my @array = ('P', 'H', 'A', 'G', 'E', 
             'P', 'H', 'A', 'G', 'E',
...
while (@array) {
   push(@words, join('', splice(@array, 0, 5)));
}

foreach (@words) {
   next unless $_ eq 'PHAGE';
   print("$_\n");
}