You definitely want to insulate the heat riser, and the burn tunnel, possibly the feed tube. Without insulation you are losing a lot of heat from the main combustion zone, especially in such a small diameter system, and you will get less complete combustion (as evidenced by your mention of chunks in the cleanout).
Insulating a steel core will cause deterioration of the metal, but with a 5" system, the degree of heat may not be so severe that it will happen fast. It may last a couple of seasons before needing to be replaced, and you will have more
experience when you do replace it. Be sure to inspect the interior regularly to see its condition.
You can probably just insulate around the existing riser with a perlite/fireclay mix, 2" thick or so. You can use light sheetmetal for an outer form. If the riser burns out, the perlite/clay will keep its shape; loose perlite would not.