We have lots of c5 sites running on Plesk so it shouldn't be a problem, ftp the files to the httpdocs folder and import a database sql file with the Databases > Import Dump tool.

How far do you get before you hit problems?

Thank you for your response. I have no doubt that you have C5 sites working on PLESK. If I started out from scratch I am sure there would be no problem. This is about moving quite a large sitehttp://www.moorparkres.org.uk
I have repeatedly carried out the actions you draw attention to and more. I have meticulously followed the instructions in the documentation for developers but without success. I will find a way eventually but the process is certainly not straightforward. I have looked for answers in the community and tried all proposed solutions I can find. I am still stuck.

When we move sites we always turn off the pretty URLs, turn off the cache, clear the cache, make a backup of the files, and make a database backup.

On the new server unzip the backup files into the webroot, upload the database to a database with the same username/password/database name credentials as the old (if this isn't possible update the credentials within c5 instead) and the site should be working - if the version of PHP is supported by the version of C5.

What version of C5 is your site? What issues are you running into? What errors are you seeing? What steps do you follow? Are you moving from one server to a server with similar specs?

After reading your more recent comment it looks like you are moving a 5.6.3.5 site, please note this site will NOT run on PHP7 unless you have done all of the core modifications to make it, or you upgrade it to 5.6.4

The Logs section (filtered for errors) in the Plesk Subscription is usually a good place to look for errors if they are not showing on screen.