CMS vs direct coding with framework for web application development

I know there has been a lot of post concerning this question, but still I did not find any of them which give a clear and good explanation. I want to develop a complete web application, with a database and some limited process in the back-end. I'm not a web app developer, but have solid programming skills with common languages (C/C++, C#, python). I thought in the beginning that using a CMS is just for "blog-like" pages, but it seems that people have been using it to develop web app as well using plugins and extensions. So my question is as follows: what is the most adapted for what I want to do ? should I use a CMS, or a code myself (using framework) ? Is there some limitations when using a CMS + extensions ? (financial for instance).