Here's the tut:
Windows 10 - Clean Install - Windows 10 Forums
Basically, what you want to do is, boot to the W10 install media, select custom install, then delete all the partitions one by one, until you have nothing left but one big unallocated drive. Proceed with the install. Don't enter a key if asked. You may have to tell it whether you want Home or Pro - be sure to select the correct one (same as you have now) or it will not activate. You won't be able to go back and forth, but why would you need to? W10 will make all the partitions it needs when it installs.
If you like, you can make an image of your current installation to your external drive using Macrium, and then, if you find you forgot to backup a file, you can always grab it from the image.