It is possible to install Evernote on MacOS 10.5.8.
As stated in the Evernote forum post referenced below, if you want to install the Evernote desktop software you have get the dmg file from the link below.
You will NOT find this link on the official Evernote download page. It is because of an official policy from Apple.
That’s the version I am using intensively every day on my 6 year old trusty MacBook.
Evernote forum post about MacOS 10.5.8:
MacOS 10.5.8 Evernote download link
Until the next time, happy evernoting!