Your input seems to match your output ... is that what you were intending? or are you trying to do something like the following:

# Choose any Range of FASTA records
# Called as perl script_name.pl --start start_line --end end_line file
+_name
# both --start and --end are optional;
# no --start => start reading from end of file, end at --end
# no --end => start reading from --start, read to end of file
# neither => print every line
use warnings;
use strict;

use Getopt::Long;
my ($start, $end) = (undef, undef);
GetOptions(
   "start=i" => \$start,
   "end=i" => \$end,
);
$/='>';
while(<>) {
   if(
     (!defined($start) || $start <= $.) &&
     (!defined($end) || $. <= $end)
   ) {
      print;
   }
}
[download]

or, here are some liners to data munge fasta records that may be closer to what you are looking for:

# Choose first N FASTA records
perl -ne 'BEGIN {$/=">";$o=0}{chomp;$o<N?(/^$/?next:print">$_"):last;$
+o++}' EXAMPLE.fa
[download]

    
# Choose the Nth FASTA record
perl -0x3E -e 'chomp(@lines = <>);print $lines[N]' EXAMPLE.fa
[download]

# Choose any Range of FASTA records
perl -0x3E -e 'chomp(@l=<>);for(STrange..ENDrange){print "record $_ is
+ >$l[$_]\n"}' EXAMPLE.fa
perl -0x3E -e 'chomp(@l=<>);print @l[STrange..ENDrange]' EXAMPLE.fa
[download]

# show the number of FASTA records in a given FASTA file
perl -0x3E -e '@l=grep/\s/,<>;print "$ARGV contains ".scalar(@l)." rec
+ords\n"' EXAMPLE.fa
[download]