By using a regular hexagonal arrangement it is simple to fit 19 identical circles into a larger circle of five times the radius with no circles overlapping. This leaves an area equal to six smaller circles uncovered. Is it possible to rearrange the 19 circles to accommodate a twentieth circle of the same size into the larger one (also with no overlapping of course)?

No, according to the information at http://www2.stetson.edu/~efriedma/cirincir/ 

