Well, isn't that just a delightful shape you've described! A figure with 5 lines of symmetry and no right angles is called a pentagon. It has those lovely symmetrical qualities that make it so pleasing to the eye. Just imagine all the wonderful ways you could paint and create with such a shape!
a pentagon
A rectangle.
An irregular quadrilateral.
rhombus
a square
a pentagon
A rectangle. Obviously the right angles are in the four corners of the rectangle. The lines of symmetry occur across the horizontal and vertical. There are no lines of symmetry on the diagonal.
A rectangle.
A pentagon has 5 lines of symmetry and no right angle.
octagon
If your asking what shape has three lines of symmetry, your answer would be an equilateral triangle. You can tell how many lines of symmetry a shape that has all angles of the same measure has by looking at it's angles. Ex., pentagon has five angles--five lines of symmetry; octagon has eight angles, eight lines of symmetry; etc.
An irregular quadrilateral.
rhombus
a square
A rectangle.
Parrallelogram (it has rotational symmetry but no lines of symmetry)
square and rectangles are technicality squares