Question 462642
Here is one such pentagon:


{{{drawing(300,300,0,10,0,10,


line(1,3,4,2),
line(4,2,7,3),
line(7,3,8,6),
line(8,6,5,8),
line(5,8,1,3),
locate(1,3,A),
locate(4,2,B),
locate(7,3,C),
locate(8,6,D),
locate(5,8,E)
)
}}}


Note that the pentagon can be any arbitrary pentagon; it does not necessarily have to be regular, convex, or cyclic.