Yes I have cleared it. Turned my computer off and on.
Tried uploaded the files individually with FileZilla. The files uploaded, overwrote existing files.
Refresh. Checked again. Still say Joomla version 1.5.2
The annoying thing is the link says 1.5.2 to 1.5.13 (zip file). However, when it downloads it says 1.5.12 to 1.5.13 and I did not notice that. So I just tried to extract that update. (nothing got screwed up I hope)
Then I just downloaded Joomla_1.5.2_to_1.5.13-Stable-Patch_Package.tar and trie to extract that file into public_htm_new and it still says version 1.5.2
I have a folder called public_html_new and that's the one I've been trying to update. It's the wrong folder. I just realised the new site I'm working on is a sub-domain so it must be inside the public_html folder for me to be able to see it online.
Ta-da! I have a folder in my public_html folder and that's the one I should have been updating (not the other folder which is not within the public_html folder).
I created a sub-domain so that so I can administer and develop the site checking what it looks like online. Then, when it's ready, I can extract the files from the sub-domain folder into a new folder in the home director and make that folder the public_html folder.