Apparently all versions including the current 14 are supported under XP: https://community.teamviewer.com/t5/Knowledge-Base/Which-operating-systems-are-supported/ta-p/24141#toc-hId--1332302068
As for me, I'm still using version 12, which I've been very happy with (12.1.12295): http://sdfox7.com/xp/sp3/EOL/TeamViewer_Setup.exe Later releases of version 12 had stability issues so I chose not to update.
You can download earlier versions of TeamViewer 13 to 10 here (Windows 10, Windows 8, Windows 7, Windows Vista, Windows XP): https://www.teamviewer.com/en/download/previous-versions/
You can download legacy versions of TeamViewer 5 to 9 here (Windows 98, Windows NT 4.0, Windows 2000): https://www.teamviewer.com/en/download/old-versions.aspx