First off, you want to use a hash to associate a given identifier (4670-5490) to a gene sequence. You will want to do something like:

my %sequences = map { $_ => undef } (
    '456-3210',
    '4670-5490',
# etc ...
);

my $current;
while (<FILE_WITH_STUFF>)
{
    chomp;

    # If this line is a sequence identifier ...
    if (/^\d+(?:-\d+)?$/)
    {
        # Clear the sequence we're parsing
        $current = undef;

        # Skip this one unless it's a sequence we're looking for
        next unless exists $sequences{$_};

        # Mark it as the one we're reading into
        $current = $_;
        next;
    }

    next unless $current;

    push @{$sequences{$current}}, $_;
}

foreach my $key (sort keys %sequences)
{
    print "$key:\n";
    print "\t$_\n" for @{$sequences{$key}};
}
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Try that and see if it does what you need. (NOTE: I did NOT test this code. It might not even compile.)