Learn Russian: Это тонкая книга.

When used to mean 'This is...' or 'These are...', the word это is a fixed intro word and stays in this default form. If you wanted to say 'This book is thin,' then the word 'this' would attach directly to the noun and match its feminine gender: Эта книга тонкая.

How would the adjective and noun look in the genitive plural, which we are learning in this lesson? For example, after the word 'five'?

After a number like 'five', you need the genitive plural. The adjective тонкая changes to тонких, using the -их ending because of the spelling rule after the letter к. The noun книга drops its ending to become книг. So, 'five thin books' is пять тонких книг.

Why does the adjective тонкая end in -ая instead of just -а like the noun?

Russian adjectives have their own set of endings to show gender and case. For feminine nouns in the nominative (subject) case, the standard adjective ending is -ая (or -яя for soft sounds). Nouns typically just end in -а or -я.

If I change this to the regular plural to say 'These are thin books', how does the spelling rule affect the adjective?