I can make even and odd pages have different footers, but I want page 4's to be different from page 2's and page 5's from page 3's.
Headers and footers change only per section. Every section can have a first page different from the rest, and odd pages different from even pages, so there are a maximum of three headers and three footers per section: first page, odd page and even page.
It seems like you have to go to the bottom of page 3 and insert a section break that begins on a new page. By default both sections will have all the same properties, and the headers and footers are linked, so you have to first go to pages 4 and 5 to break
that "link to previous" as it's called. Then you can change page 4's and 5's header and footer without chaning 2's and 3's.
The somewhat more techie way is to go into the odd and even headers and put in an IF fieldcode whose condition depends on the PAGENUMBER field code, but that gets messy very easily...