awk -v pat="pattern_" -v before=5 -v after=6 '
FNR==NR && $0 ~ pat {b=NR-before;a=NR+after;next}
FNR!=NR && (FNR<b || FNR>a) {print FNR ": " $0}
' file file

 # prepare file for testing:
n=0; fl=for_removing_lines.txt; rmv_lbl="point of removing"; rm $fl; 
while [ $n -le 20 ];do  
   (( n++ )); echo "line $n">>$fl; 
   if [ $n -eq 10 ]; then 
      echo $rmv_lbl>>$fl; 
   fi; 
done;

 # geting line numbers to statr and END remuving 
pnt_ln=`nawk -v srch="$rmv_lbl" '{if($0~srch) print NR; }' $fl`; 
((rmv_st=pnt_ln-6)); 
((rmv_end=pnt_ln+6));     echo $pnt_ln, $rmv_st, $rmv_end

 # printing file without 6 lines before and after label line
nawk -v st=$rmv_st -v end=$rmv_end '{if( (NR <= st)||(NR >= end) ) print $0; }' $fl

#!/usr/bin/env sh

# @(#) s3       Demonstrate deleting a range with line editor.

#  ____
# /
# |   Infrastructure BEGIN

echo
set -o nounset

debug=":"
debug="echo"

## The shebang using "env" line is designed for portability. For
#  higher security, use:
#
#  #!/bin/sh -

## Use local command version for the commands in this demonstration.

EDITOR=ex
EDITOR=ed

set +o nounset
echo "(Versions displayed with local utility \"version\")"
version >/dev/null 2>&1 && version =o $(_eat $0 $1) $EDITOR
set -o nounset

echo

FILE=data1
cp sacred $FILE
echo " Input file $FILE:"
cat $FILE

before=5
after=6
pattern="pattern"

# |   Infrastructure END
# \
#  ---

echo
echo " Output from editor $EDITOR:"
$EDITOR <<EOF $FILE
/$pattern/-${before},/$pattern/+${after}d
w
q
EOF
echo
echo " Output file $FILE:"
cat $FILE

exit 0

% ./s3

(Versions displayed with local utility "version")
Linux 2.6.11-x1
GNU bash, version 2.05b.0(1)-release (i386-pc-linux-gnu)
GNU ed version 0.2

 Input file data1:
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
pattern
1
2
3
4
5
6
7
8
9
10

 Output from editor ed:
60
25

 Output file data1:
-10
-9
-8
-7
-6
7
8
9
10