If I get this right, a size 5 ring has it's inner diameter of a hair less than 16mm (15.7 by charts). Add a 1.5-2mm thick shank and the exterior diameter of the ring gets to 19-20mm. It's not common to set the diamonds "flat" - the sides are set an angle relative to the center stone (this is about the alignment of the tables), so they take less room than the actual added legth.
The three stones will definitely cover the finger and give the jeweler the task to minimize the space taken by prongs and what not in order to fit the three together just so
with NO room whatsoever between the center and the sides.
In the Vatche picture, the length of the pears is about 60% of the center's diameter, for ref.
wel... the upper one has the sides shorter than the center. The drawing below shows what a ring may look like with the pears as long as the side of the princess cut.