This code does it in a fairly straightforward way (although I like the grep solution best).

#!/usr/bin/perl
use strict;
use warnings;

my $line;
my $num_lines = 0;

while ($line = <DATA>) {
    $num_lines = 4 if $line =~ /^id:/;
    if ($num_lines > 0) {
        print $line;
        $num_lines--;
    }
}
exit 0;

__DATA__
John, Doe Michael
id:1234567890123 library:ACME
City, state:PUEBLO, CO
Phone:719-555-555
Street:1610 Sorrow AVE APT D
Zip: 81004

Jane, Doe Michael
id:1234567890124 library:ACME
City, state:PUEBLO, CO
Phone:719-222-555
Street:1610 Happy AVE APT D
Zip: 81006
[download]

Andas the one-liner it started out as (much love for -n and $_ in the right context):

perl -n -e '$n = 4 if /^id:/; if ($n) { print; $n--; }' your_data_file
[download]