Code for a nice Venn 5.

pp=RootReduce[2CirclePoints[5]/(EuclideanDistance@@CirclePoints[5][[{1,2}]])];
sp=Join[Table[2.12CirclePoints[10][[Mod[n-2,10,1]]]+pp[[2]],{n,1,9}],
Table[1.05CirclePoints[10][[Mod[n-6,10,1]]]+pp[[4]],{n,1,7}]];
Graphics[{AbsoluteThickness[2],Table[BSplineCurve[sp.RotationMatrix[2 k Pi/5], SplineClosed-> True],{k,0,4}]},ImageSize->600]