Hello, gwen01!
Divide a line segment into five equal parts using a compass and straightedge.
Given a line segment AB diagonally (say, to the upper-right).
Draw a horizontal line AC to the right. Code:
B
*
*
*
*
*
*
*
*
*
*
A * - - - - - - - - - - - - - - - - - C
On AC, mark off five equal segments: .$\displaystyle AP = PQ = QR = RS = ST$ Code:
B
*
*
*
*
*
*
*
*
*
*
A * - - + - - + - - + - - + - - + - - C
P Q R S T
Draw segment BT. Code:
B
*
* \
* \
* \
* \
* \
* \
* \
* \
* \
A * - - + - - + - - + - - + - - + - - C
P Q R S T
Through P, Q, R, S construct lines parallel to BT,
. . intersecting AB at W, X, Y, Z. Code:
B
*
Z * \
o \
Y * \ \
o \ \
X * \ \ \
o \ \ \
W * \ \ \ \
o \ \ \ \
* \ \ \ \ \
A * - - + - - + - - + - - + - - + - - C
P Q R S T
Then: .$\displaystyle AW = WX = XY = YZ = ZB $
Nice job, wingless!