Official and reputable third-party sources offer archives of these older versions:

Another alternative for sourcing previous AnyDesk releases if you need a specific build not found elsewhere. Installation Steps for Older Macs

On OS X 10.9.5, you may need to go to System Preferences > Security & Privacy . Ensure that AnyDesk is allowed to run under the "General" tab and check "Accessibility" permissions under the "Privacy" tab to allow remote control.