It shouldn't be any problem to upgrade from 4.5.3 to 4.7.0.  Firstly, make sure you backup your files and database before you do anything.

It is usually inadvisable to use the upgrade package between major releases, I would suggest using the 4.7.0 Install package, which will require you to migrate your web.config, since there are usually changes in the web.config between major versions.

Once you've backed up everything, you should just need to copy the install package over your website, reset the file permissions on the website, copy your connection strings, machine keys, and any custom sections into the new web.config, then hit the site and it should upgrade for you.

Hope that helps,