What two big ideas does Nick have in chapters 5 and 6 of Andrew Clements' Frindle? Is he right or wrong to act out those ideas?

In chapter 5 of Andrew Clements' Frindle, Nick's first big idea is to question who decides the meanings of words. This idea gives him inspiration for his next big idea in chapter 6 and serves as the basis of the book. In questioning who decides what words mean, Nick shows his ability to question authority, think creatively, and make major changes in the world, which are all abilities Mrs. Granger sees in Nick and approves of.
 
Nick questions who determines the meanings of words when he asks Mrs. Granger, "[W]ho says d-o-g means the thing that goes woof and wags its tail?." To his surprise, Mrs. Granger replies that Nick himself and all of society around him determine the meanings of words because they "all agree" that a specific word means something specific. Nick's question shows that he is able to think creatively; he's not willing to accept that something is correct just because society says it's correct. This is the sort of creative thinking that leads to big changes within society.

Mrs. Granger's answer that Nick chooses the meanings of words inspires him to invent his own word in the next chapter, just as he invented the word gwagala when he was a toddler to mean music. In Nick's mind, if Nick himself determines meanings of words, then who says he can't decide that a pen should really be called a frindle, which is his second big idea. Mrs. Granger initially objects to his invention of a new word because, in her mind, the meanings of words are not arbitrary; meanings of words were developed over a long period of history based on specific reasons. For example, the word pen stems from the Latin word pinna, which means feather since people used to write with pens made from feathers, called quill pens.

Since Nick is challenging authority and hundreds of years of history by inventing his own word, Nick is causing trouble. Clements shows Nick is not wrong to challenge authority and hundreds of years of established ideas, however, because those are the only kinds of challenges that make significant and deeply needed changes within society; Mrs. Granger shows she knows Nick is the sort of person who will initiate big changes when, on the last day of school, she says to him, "Now you go out there and have a wonderful summer. And I expect to hear remarkable things about you, young man" (Chapter 15). Therefore, though Nick created trouble by acting on his big ideas, he was perfectly right to do so.