My experience with constructing an inscribed pentagon began when I found' it using a % circle. The units of regular intervals of 100 points with 20 that were numbered in intervals of 5 was a 'readymade. I used it to teach children to make geometric constructions using a straight edge.
My students could construct a rotation of 4 inscribed pentagons very easily. They could inscribe as many pointed stars! They could observe and visualize many attributes of the geometric circle using these readymades which were copier printed from masters.
I have for many years and in many classrooms been able to introduce 4th and 5th graders to DO 'geometry the old fashioned way'. That is with a straight edge and these readymade Degree and Percentage circles. It enabled students to make wonderfully kaleidoscopic designs based on inscribed polygons.
Of the 3 shapes I used, the square was the easiest, the hexagon more challenging, requiring dividing 100 approximately in 3rds, then the 3rds bisected into 6 and then 12 regular intervals.
I found that a clear plastic circle, (the extruded kind) one having an extruded point at its center. Such used to be obtained at the salad bar at supermarkets. It worked handily as a compass with but a single radius. Making a dot on the sheet of paper and placing the plastic circle to align with it children drew geometric designs with the disc and their straight edges (usually produced in quantities as needed in my art room cutting board. They made Pennsylvania Dutch hex signs and therefrom hexagons, and had discussions as to whether or not the clocks 2=12 numbers might have been the origin of the angles totaling the circle's 360 degrees.
Making kaleidoscopic designs with pentagons was ands for older and more experienced geometers.
I should conjecture that ALL regular polygons are inscribable. Beginning with the 3gon, (4gon, 5gon, 6gon, 7gon, etc.) every successive whole number can be rendered, be truly regarded as valid a regular polygon. And the set of such polygons goes on to infinity. In the Platonic and Euclidean schema the intervals paradoxically can be inscribed ad finitum!