Chapter 5 is mainly documents written by Galileo in 1615, answering his critics at trial. Much of it concerns interpretation of Scripture, and how a robust, honest, and defensible Catholicism will require a figurative interpretation of passages whose literal meaning would contradict observations. However, in the midst of that, he also challenges the argument that there's no point in believing Copernicus if even Copernicus regarded his model as only a tool for calculation. Galileo elides questions of what Copernicus "really" thought (as high as his self-esteem was, Galileo did not consider himself capable of performing necromancy and consulting the dead Copernicus). Instead, he noted that in many ways it's the geocentric model that is a calculational tool. The heliocentric model enables fairly simple calculations, but if one wishes to put those results into a form that can be compared with observation, one must switch to a geocentric frame. This blurs the distinction between steps taken for convenience and steps taken to reflect reality. (Einstein finally shattered that distinction altogether.)
I like this argument. I'm not, however, quite so favorable towards another argument. He also tries the argument that everyone who favors the heliocentric model started off favoring the geocentric model, so they must have had a good reason to change their minds. Furthermore, only smart and informed people will even think of adopting the heliocentric model, because they will understand the subtle observational and theoretical arguments for it, whereas less informed people (and well-informed but cautious people) will reject it.
I don't like that argument. I've met smart people who believed all sorts of dumb things for all sorts of dumb reasons, and I've met ignorant people who embraced alternative viewpoints simply because they wanted to be in the opposition, not because they actually understood the merits of the idea. I get that Galileo was on trial and trying to persuade people rather than trying to carefully strike at deep truths of human psychology. However, I am nonetheless unimpressed by the argument. Surely he must have known that fools were, are, and always will be everywhere.