What sounds odd here is why you have an EPUB named "Chapter 5". An EPUB book would normally be named with the book title and contain (amongst other things) a number of files such as Chapter1.html, Chapter2.html, Chapter3.html, Chapter4.html, Chapter5.html together with other stuff that "hold it all together".
You are right that just adding a file to an existing EPUB is not a simple as just "dropping it in" - it needs to use the same css elements as the other files and reference the same .css files in order that that chapter will be in the right place when you read the book and look the same as the rest of the book. You will also need to regenerate the Table of Contents for the book to reference the "new" file.
It looks like you have found the right tool for doing the job you want but really need to understand what you are carving up before starting out on open heart surgery. Try examining a few books with Sigil to see how the bits of an EPUB interact with each other (how to change the Chapter order and how to build the TOC and most important how the individual html (or xml) files interact with the css (style) files to give a consistent appearance.
There is an explanation of how to build an EPUB "by hand" at
http://www.ibm.com/developerworks/xm.../section3.html which might make things a little clearer.
HTH BobC