In the diagram below, AB is a diameter of circle O. Point C is drawn such that BC is tangent to circle O, and AB=BC. A point F is selected on line AB and a point D is selected on circle O such that ∠CDF=90∘. Line BD is then extended to point E such that AE is tangent to circle O. Given that AE=5, calculate the length of AF. (Diagram not to scale)
[asy]
size(120);
pair A,O,F,B,D,EE,C;
A=(-5,0);
O=(0,0);
B=(5,0);
EE=(-5,6);
F=(3.8,0);
D=(-2.5,4.33);
C=(5,10);
dot(A^^O^^B^^EE^^F^^D^^C);
draw(circle(O,5));
draw(A--EE--F--cycle);
draw(D--B--C--cycle);
draw(A--B);
label("A",A,W);
label("O",O,S);
label("B",B,E);
label("F",F,S);
label("E",EE,N);
label("D",D,N);
label("C",C,N);
[/asy]
<spanclass=′latex−bold′>(A)</span>29<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>33<spanclass=′latex−bold′>(D)</span>7<spanclass=′latex−bold′>(E)</span>impossible to determine