Draw a figure!!!!!!
The central angle is 360/8=45 (not as you listed!)
The isosceles triangle formed by the center and the ends of a base has altitude 5.
1/2 the vertex angle is 22.5 degrees.
1/2 of the base is 5*tan 22.5°
Therefore the base is 10*tan 22.5°=10*.408=4.08 feet
Your problem didn't ask for the area, but your answer seems to be looking for it.
The area of the isosceles triangle mentioned above is (1/2)*4.08*5 and there are 8 of these in the octagon,
i.e.the area is 4*4.08*5.