awk
to the rescue!
to print with the pattern line (total 6 lines)
$ awk '/^####PATTERN/{c=6} c&&c--' file
####PATTERN#######
#Line1
#Line2
#Line3
#Line4
#Line5
to skip pattern and print the next five lines
$ awk 'c&&c--; /^####PATTERN/{c=5}' file
#Line1
#Line2
#Line3
#Line4
#Line5