I wish to create 5 identical white circles of some lesser radius, which I will place on top of the black circle and completely obscure (cover) the black circle.

What is the smallest radius which I can make the smaller circles and still meet my requirement?

What I said was "the radius ratio of .609383:1 is given as optimal whereas the pentagon approach gives .618034:1." And, yes, .618034.. is the reciprocal of phi which not too surprisingly arises in the symmetrical case where a regular pentagon is involved.

The .609383 optimal case is not symmetrical, and the documented solutions where it is found are messy to say the least -- so messy, in fact, that they raise the difficulty level to 4+ if not indeed to 5, IMHO. Good luck all (Jer especially) in your attempts to nail down the .609383 on your own.