I upgraded from Zen-cart 1.39h to 1.5 using Softaculous application my hosting company provides.
It was a very simple upgrade.
After upgrading my home page displays following message:
Congratulations! You have successfully installed your Zen Cart« E-Commerce Solution.
Welcome Guest! Would you like to log yourself in?
Also categories has link to .jpg file.
I have backed up the database and site.