in reply to Search String - next line

As a one-liner 

perl -ne "$n = $.if /line 05/; print if $n and $. == ( $n + 4 )" numbe
+red.dat

[download]
Substitute your match criteria for /line 05/, the number after for the constant 4 and the name of your file at the end.

As a program 

#! perl -sw
use strict;
my $p;
while (<DATA>) {
    $p = $. if /$ARGV[0]/;
    print if $p and $. == ( $p + $ARGV[1] );
}
=pod output (comment only)
c:\test>210984 "line 05" 4
line 09

c:\test>
=cut
__DATA__
line 01
line 02
line 03
line 04
line 05
line 06
line 07
line 08
line 09
line 10
line 11
line 12
line 13
line 14
line 15
line 16
line 17
line 18
line 19
line 20

[download]
Nah! You're thinking of Simon Templar, originally played (on UKTV) by Roger Moore and later by Ian Ogilvy

In Section Seekers of Perl Wisdom