If a molecule has four bonded pairs and two lone pairs it is square planar, eg XeF4.
In the case of five pairs, all of the regions of electron density repel one another to give the basic electronic shape as a trigonal bipyramid eg PCl5.
If one of the pairs is a lone pair then this repels the others a little more than they repel themselves.
As the lone pair occupies one of the equatorial slots to minimise interactions with other pairs (in trigonal bipyramidal there are three equatorial and two axial positions) this then produces a distorted umbrella or square pyramid.
Sorry about your book, but it isn't correct - who is the author?