Indesign Page Insert Issue

There are tools in InDesign that allow you to change paper size and have most-or-all of your elements stick to margins. However, those tools usually work best when you start your document with those assumptions in mind. However, I can't suggest that you use them, as your explanation of your challenge is missing about half the information we'd need in order to make meaningful suggestions (besides the obvious "just pay a designer with experience in this area for a few hours of their time").

But, assuming that you reaally want to learn about all of this print production stuff yourself: if you're saying "A5" and are correct about that (are you sure you don't mean A4?) then you're working on a booklet, right? A5 is about half the size of one sheet of landscape 8.5x11. In order for your booklet to print correctly, you must have a number of pages that is a multiple of four. 

When two pages are "stuck together" this is called a "spread." When you started your document, you clearly chose "spreads" even if you didn't mean to, because if you chose a single-page layout, then you'd have "right" and "left" margin settings instead of "inside" and "outside." Can you take a screenshot of your Pages panel, with all of your pages visible? I don't know if you can or not, because I don't know how long your document is, but if you're working with some reasonable number of pages (16? 24?) you should be able to do so. 

Also, in the Pages panel, if you click on the little flyout menu button in the upper right hand corner, you can tell us if "Allow document pages to shuffle" and "Allow selected spread to shuffle" are checked. These settings will influence what happens when you add a single page to a document set up for spreads.