Is it possible to transfer an OEM Windows 10 license?

I want to change the drive on my laptop to an SSD. I use Windows 10, and I have two options :

• clone the HDD to an SSD
• install a fresh copy of Windows 10 on the new drive

Since I would like to use the opportunity of the move to freshen up my 5 years old installation, I would like to go the reinstall way.

The first problem is the installation media for Windows 10. It would seem that it is possible to create install media directly from Microsoft.

The second problem is the license: is there a way to transfer it from my existing installation?

There is no need to "transfer the license". Licenses are attached to motherboards, not to hard drives, you can just install a fresh copy of Windows on your new drive and use the same OEM license. You mention a 5 years old installation, which I can only assume you did the painful windows 7 to Windows 8 to Windows 8.1 to Windows 10 upgrade. In which case I will encourage you to download a fresh ISO from Windows, and do the install either with a USB or disc, then just use your key, should be fine.