You could use...
find /path/to/specific/directory -maxdepth 1 -type f -name "file.txt" -exec sed -i.bak '5,10 d' '{}' \;
Explanation:
-maxdepth 1
don't look in any subdirectories of the specified directory
-type f
only find files, not directories
-exec
do the following command to the found files
sed '5,10 d'
delete lines from 5 to 10
-i.bak
modify the file itself rather than printing to stdout but make a backup copy of the original file with the extension .bak
EDIT: although actually if you know exactly where the file is and what it's called you can obviously do
sed -i.bak '5,10 d' /path/to/file.txt
silly me...