The Five Pennies

Here is a really hard puzzle, and yet its conditions are so absurdly simple. Every reader knows how to place four pennies so that they are equidistant from each other. All you have to do is to arrange three of them flat on the table so that they touch one another in the form of a triangle, and lay the fourth penny on top in the centre. Then, as every penny touches every other penny, they are all at equal distances from one another. Now try to do the same thing with five pennies--place them so that every penny shall touch every other penny--and you will find it a different matter altogether.

Its source prints no answer for this problem, so there's nothing to check against.

H. E. Dudeney, Amusements in Mathematics (1917) · No. 419