Exercise 1-3-1 and 1-3-2

In the two mentioned exercises, I’m confused by the chord progression in them.  The last two measures of the first exercise has a V6/4 chord go into a 5/3….but I’m really confused by this.  The V6/4 looks like a C chord not a G chord, especially since the notes are G-C-E-G.  Why is it a V6/4?  The 5/3 part looks like a G chord so I’m assuming the 5/3 is an inversion mark of some sort.  and then it resolves to a I.
The second exercise does a similar thing only it starts on the second beat of the measure.  This time the 5/3 looks to be a C chord this time instead of a G chord, so why is it not an I with an inversion?
Any help with this would be amazing.
Thank You,
Brian